Publication list for Brendan McKay.

Theses.

  1. B. D. McKay, Backtrack Programming and the Graph Isomorphism Problem, Master of Science thesis, Unversity of Melbourne, 1976. PDF.
  2. B. D. McKay, Topics in Computational Graph Theory, PhD thesis, University of Melbourne, 1980. PDF.

Published technical articles.

  1. C. D. Godsil and B. D. McKay, Some computational results on the spectra of graphs, Combinatorial Mathematics IV, Lecture Notes in Mathematics, 560 (Springer-Verlag, Berlin, 1976) 73-92. PDF.
  2. C. D. Godsil and B. D. McKay, Products of graphs and their spectra, Combinatorial Mathematics IV, Lecture Notes in Mathematics, 560 (Springer-Verlag, Berlin, 1976) 61-72. PDF.
  3. C. D. Godsil, D. A. Holton and B. D. McKay, The spectrum of a graph, Combinatorial Mathematics V, Lecture Notes in Mathematics, 622 (Springer-Verlag, Berlin, 1977) 91-117. PDF.
  4. C. D. Godsil and B. D. McKay, A new graph product and its spectrum, Bulletin of the Australian Mathematical Society, 18 (1978) 21-28. PDF.
  5. B. D. McKay, Computer reconstruction of small graphs, Journal of Graph Theory, 1 (1977) 281-283. PDF.
  6. B. D. McKay, On the spectral characterisation of trees, Ars Combinatoria, 3 (1977) 219-232. PDF.
  7. B. D. McKay, Backtrack programming and isomorph rejection on ordered subsets, Ars Combinatoria, 5 (1978) 65-99. PDF.
  8. B. D. McKay, Computing automorphisms and canonical labellings of graphs, Combinatorial Mathematics, Lecture Notes in Mathematics, 686 (Springer-Verlag, Berlin, 1978) 223-232. PDF.
  9. B. D. McKay, Transitive graphs with fewer than twenty vertices, Mathematics of Computation, 33 (1979) 1101-1122 and microfiche. Main part; Data (includes what appeared in the microfiche).
  10. B. D. McKay, Hadamard equivalence via graph isomorphism, Discrete Mathematics, 27 (1979) 213-216. PDF.
  11. B. D. McKay and R. G. Stanton, Isomorphism of two large designs, Ars Combinatoria, 6 (1978) 87-90.
  12. C. D. Godsil and B. D. McKay, Spectral conditions for the reconstructibility of a graph, Journal of Combinatorial Theory (B), 30 (1981) 285-289. PDF.
  13. C. D. Godsil and B. D. McKay, Feasibility conditions for the existence of walk-regular graphs, Linear Algebra and its Applications, 30 (1980) 51-61. PDF (with erratum).
  14. B. D. McKay and R. G. Stanton, The current status of the generalised Moore graph problem, Combinatorial Mathematics VI, Lecture Notes in Mathematics, 748 (Springer-Verlag, Berlin, 1979) 21-31. PDF (with erratum).
  15. C. D. Godsil and B. D. McKay, The dimension of a graph, Quarterly Journal of Mathematics, 31 (1980) 423-437.
  16. D. McCarthy and B. D. McKay, Transposable and symmetrizable matrices, Journal of the Australian Mathematical Society (Series A), 29 (1980) 469-474. PDF.
  17. B. D. McKay and R. G. Stanton, Some graph isomorphism computations, Ars Combinatoria, 9 (1980) 307-313.
  18. C. D. Godsil and B. D. McKay, Graphs with regular neighbourhoods, Combinatorial Mathematics VII, Lecture Notes in Mathematics, 829 (Springer-Verlag, Berlin, 1980) 127-140.
  19. C. Colbourn and B. D. McKay, A correction to Colbourn's paper on the complexity of matrix symmetrizability, Information Processing Letters, 11 (1980) 96-97. PDF.
  20. B. D. McKay, The expected eigenvalue distribution of a large regular graph, Linear Algebra and its Applications, 40 (1981) 203-216. PDF.
  21. B. D. McKay, Practical graph isomorphism, 10th. Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, 1980); Congressus Numerantium, 30 (1981) 45-87. scan.
  22. B. D. McKay, Spanning trees in random regular graphs, Third Caribbean Conference on Combinatorics and Computing, (University of West Indies, 1981) 139-143. PDF.
  23. D. A. Holton, B. D. McKay, M. D. Plummer and C. Thomassen, A nine-point theorem for 3-connected graphs, Combinatorica, 2 (1982) 53-62.
  24. B. D. McKay, Subgraphs of random graphs with specified degrees, Congressus Numerantium, 33 (1981) 213-223. PDF.
  25. D. A. Holton, B. D. McKay and M. D. Plummer, A corollary to Perfect's theorem, Combinatorial Mathematics IX, Lecture Notes in Mathematics, 952 (Springer-Verlag, Berlin, 1982) 294-299. PDF.
  26. B. D. McKay, Spanning trees in regular graphs, European J. Combinatorics, 4 (1983) 149-160. PDF.
  27. C. D. Godsil and B. D. McKay, Constructing cospectral graphs, Aequationes Mathematicae, 25 (1983) 257-268. PDF.
  28. P. Erdos, R. L. Hemminger, D. A. Holton and B. D. McKay, On the chessmaster problem, in Progress in Graph Theory, (Academic Press, 1984) 532-536. scan.
  29. B. D. McKay, Asymptotics for 0-1 matrices with prescribed line sums, in Enumeration and Design, (Academic Press, 1984) 225-238. PDF
  30. B. D. McKay and I. G. Tollis, A resource location problem on graphs, Congressus Numerantium, 40 (1983) 223-234. PDF
  31. B. D. McKay, Applications of a technique for labelled enumeration, Congressus Numerantium, 40 (1983) 207-221. PDF
  32. R. L. Hemminger and B. D. McKay, More on the chessmaster problem, Congressus Numerantium, 40 (1983) 442-444.
  33. C. D. Godsil and B. D. McKay, Asymptotic enumeration of Latin rectangles, Bulletin of the American Mathematical Society, 10 (1984) 91-92.
  34. B. D. McKay and N. C. Wormald, Automorphisms of random graphs with specified degrees, Combinatorica, 4 (1984) 325-338. PDF.
  35. P. Eades and B. D. McKay, An algorithm for generating subsets of fixed size with a strong minimal change property, Information Processing Letters, 19 (1984) 131-133. PDF.
  36. W. Liang and B. D. McKay, Fast parallel algorithms for testing k-connectivity of directed and undirected graphs, IEEE First Intern. Conf. on Alg. and Arch. for Parallel Proc., April 1995 (ed. V. L. Narasimhan), 437-441. PDF.
  37. R. A. Wright, B. Richmond, A. Odlyzko and B. D. McKay, Constant time generation of free trees, SIAM J. Computing, 15 (1986) 540-548. PDF.
  38. R. L. Hemminger and B. D. McKay, Integer sequences with proscribed differences and bounded growth rate, Discrete Math., 55 (1985) 255-265. PDF.
  39. B. D. McKay, Asymptotics for symmetric 0-1 matrices with prescribed row sums, Ars Combinatoria, 19A (1985) 15-26. PDF.
  40. B. Bollobas and B. D. McKay, The number of matchings in random regular graphs and bipartite graphs, J. Combinatorial Theory (B), 41 (1986) 80-91. PDF.
  41. B. D. McKay and G. F. Royle, Constructing the cubic graphs on up to 20 vertices, Ars Combinatoria, 21A (1986) 129-140. PDF.
  42. D. A. Holton and B. D. McKay, Cycles in 3-connected cubic planar graphs II, Ars Combinatoria, 21A (1986) 107-114. PDF.
  43. P. Eades, B. D. McKay and N. C. Wormald, On an edge crossing problem, Proceedings of 9th. Australian Computer Science Conference, Canberra (1986), 327-334. PDF.
  44. D. A. Holton, B. Manvel and B. D. McKay, Hamiltonian cycles in cubic 3-connected bipartite planar graphs, J. Combinatorial Theory (B), 38 (1985) 279-297. PDF.
  45. B. E. Eichinger, D. M. Jackson and B. D. McKay, Generating function methods for macromolecules at surfaces, I. One molecule at a plane surface, J. Chem. Phys., 85 (1986) 5299-5305. PDF.
  46. B. D. McKay, Independent sets in regular graphs of high girth, Proc. Australia-Singapore Joint Conference on Information Processing and Combinatorial Mathematics (Singapore, 1986). Ars Combinatoria, 23A (1987) 179-185. PDF.
  47. R. P. Brent and B. D. McKay, Determinants and ranks of random integer matrices over Zm, Discrete Math., 66 (1987) 35-49. PDF.
  48. D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combinatorial Theory (B), 45 (1988) 315-319. PDF.
  49. C. W. Johnson, B. D. McKay and V. Sharma, Further methods for detecting plagiarism in student programs, Australian Computer Science Communications, 9 (1987) 282-293.
  50. C. Colbourn and B. D. McKay, Cubic neighbourhoods in triple systems, Annals of Disc. Math., 34 (1987) 119-136.
  51. B. E. Eichinger, D. M. Jackson and B. D. McKay, Generating function methods for macromolecules at surfaces, II. one molecule between two planes, J. Chem. Phys., 88 (1988) 5171-5180. PDF.
  52. R. P. Brent and B. D. McKay, Determinants of random symmetric matrices over Zm, Ars Combinatoria, 26-A (1988) 57-64. PDF.
  53. C. D. Godsil and B. D. McKay, Asymptotic enumeration of Latin rectangles, J. Combinatorial Theory, Ser. B, 48 (1990) 19-44. scan with corrections (PDF).
  54. B. D. McKay, On Littlewood's estimate for the binomial distribution, Adv. Appl. Prob., 21 (1989) 475-478. PDF.
  55. B. D. McKay and N. C. Wormald, Asymptotic enumeration by degree sequence of graphs of high degree, European J. Combin., 11 (1990) 565-580. PDF.
  56. B. D. McKay, On the shape of a random acyclic digraph, Math. Proc. Cambridge Phil. Soc., 106 (1989) 459-465. PDF.
  57. B. D. McKay and N. C. Wormald, Uniform generation of random regular graphs of moderate degree, J. Algorithms, 11 (1990) 52-67. PDF.
  58. B. D. McKay, The asymptotic numbers of regular tournaments, eulerian digraphs and eulerian oriented graphs, Combinatorica, 10 (1990) 367-377. PDF.
  59. B. D. McKay and G. F. Royle, The transitive graphs with at most 26 vertices, Ars Combinatoria, 30 (1990) 161-176. PDF. The graphs can be obtained here.
  60. Liu Bolian, B. D. McKay, N. C. Wormald and Zhang Ke Min, The exponent set of symmetric primitive (0,1)-matrices with zero trace, Linear Alg. Appl., 133 (1990) 121-131.
  61. B. D. McKay and N. C. Wormald, Asymptotic enumeration by degree sequence of graphs with degrees o(sqrt(n)), Combinatorica, 11 (1991) 369-382. PDF without figures.
  62. E. A. Bender, E. R. Canfield and B. D. McKay, The asymptotic number of labeled connected graphs with a given number of vertices and edges, Random Structures and Algorithms, 1 (1990) 127-169. PDF.
  63. B. D. McKay and N. C. Wormald, Uniform generation of random Latin rectangles, J. Combinatorial Mathematics and Combinatorial Computing, 9 (1991) 179-186. PDF.
  64. M. Jerrum, B. D. McKay and A. Sinclair, When is a graphical sequence stable?, in Random Graphs Vol 2 (eds. A. Frieze and T. Luczak; Wiley-Interscience 1992) 101-116. PDF.
  65. B. D. McKay and C. E. Praeger, Vertex-transitive graphs which are not Cayley graphs, I., J. Austr. Math. Soc. (Series A), 56 (1994) 53-63. PDF.
  66. B. D. McKay and S. P. Radziszowski, A new upper bound for the Ramsey number R(5,5), Australasian J. Combinatorics, 5 (1991) 13-20.
  67. B. D. McKay and S. P. Radziszowski, The first classical Ramsey number for hypergraphs is computed, Proceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'91, San Francisco, (1991) 304-308. PDF.
  68. B. D. McKay and Zhang Ke Min, The value of the Ramsey number R(3,8), J. Graph Theory, 16 (1992) 99-105. dvi; ps.gz.
  69. E. A. Bender, E. R. Canfield and B. D. McKay, Asymptotic properties of labelled connected graphs, Random Structures and Algorithms, 3 (1992) 183-202. PDF.
  70. R. Faudree and B. D. McKay, A conjecture of Erdos and the Ramsey number r(W6), J. Combinatorial Math. and Combinatorial Comput., 13 (1993) 23-31. PDF.
  71. E. A. Bender, E. R. Canfield and B. D. McKay, The asymptotic number of weakly-connected digraphs with a given number of vertices and edges, Australasian J. Combin., 6 (1992) 119-124.
  72. N. Calkin, A. Frieze and B. D. McKay, On subgraph sizes of random graphs, Combinatorics, Probability and Computing, 1 (1992) 123-134.
  73. B. D. McKay and S. P. Radziszowski, Linear Programming in some Ramsey problems, J. Combinatorial Theory, Ser. B, 61 (1994) 125-132.
  74. B. D. McKay and S. P. Radziszowski, R(4,5)=25, J. Graph Theory, 19 (1995) 309-322. PDF.
  75. J. H. Dinitz, D. K. Garnick and B. D. McKay, There are 526,915,620 nonisomorphic one-factorizations of K(12), J. Combinatorial Designs, 2 (1994) 273-285. PDF.
  76. J. L. Low, S. M. Lewis, B. D. McKay and P. Prescott, Computational issues for cross-over designs subject to dropout, Proceedings in Computational Statistics, 1994, 423-428.
  77. A. Frieze and B. D. McKay, Multicoloured trees in random graphs, Random Structures and Algorithms, 5 (1994) 45-56.
  78. Jun Hu, A. H. MacDonald and B. D. McKay, Correlations in two-dimensional vortex liquids, Physical Review B, 149 (1994) 15263-15270. PDF.
  79. B. D. McKay and X. Wang, Asymptotic enumeration of tournaments with a given score sequence, J. Combinatorial Theory, Ser. A, 73 (1996) 77-90 PDF.
  80. B. D. McKay and S. P. Radziszowski, There are no 4-(12,6,6) designs, in Computational and Constructive Design Theory (ed. W. Wallis) (Kluwer Academic Publ., Dordrecht, 1996), 177-188. dvi; ps.gz.
  81. G. Brinkmann, B. D. McKay and C. Saager, The smallest cubic graphs of girth 9, Combinatorics Probability and Computing, 4 (1995) 317-330. PDF.
  82. B. D. McKay and C. E. Praeger, Vertex-transitive graphs which are not Cayley graphs, II., J. Graph Theory, 22 (1996) 321-334 PDF.
  83. W. Liang and B. D. McKay, Fast parallel algorithms for testing k-connectivity of directed and undirected graphs, IEEE First Intern. Conf. on Alg. and Arch. for Parallel Proc., April 1995 (ed. V. L. Narasimhan), 437-441.
  84. R. A. Aldred, B. D. McKay and N. C. Wormald, Small hypohamiltonian graphs, J. Combinatorial Math. Combinatorial Comput., 23 (1997) 143-152. PDF.
  85. B. D. McKay and S. P. Radziszowski, Towards deciding the existence of 2-(22,8,4) designs, J. Combin. Math. and Combin. Computing, 22 (1996) 211-222. dvi; ps.gz.
  86. B. D. McKay and E. Rogoyski, Latin squares of order ten, Electronic J. Combinatorics, 2 (1995) #N5 (4 pages). Link to E-JC.
  87. Weifa Liang, B. D. McKay and Hong Shen, NC algorithms for dynamically solving the all pairs shortest path problem and related problems, Information Processing Letters, 58 (1996) 149-155.
  88. B. D. McKay, Small graphs are reconstructible, Australasian J. Combinatorics, 15 (1997) 123-126. PS; PDF.
  89. F. Bussemaker, I. Kaplansky, B. D. McKay and J. J. Seidel, Determinants of matrices of the conference type, Linear Algebra Applic., 261 (1997) 275-292.
  90. B. D. McKay and S. P. Radziszowski, Subgraph counting identities and Ramsey numbers, J. Combinatorial Theory, Ser. B, 69 (1997) 193-209. PDF.
  91. B. D. McKay and R. W. Robinson, Asymptotic enumeration of Eulerian circuits in the complete graph, Combin. Prob. Comput., 7 (1998) 437-449. PDF.
  92. B. D. McKay and N. C. Wormald, The degree sequence of a random graph. I. The models, Random Structures and Algorithms, 11 (1997) 97-117. PDF.
  93. B. D. McKay and I. M. Wanless, Maximising the permanent of (0,1)-matrices and the number of extensions of Latin rectangles, Electronic J Combinatorics, 5 (1998) #R11 (20 pages). Link to E-JC.
  94. D. Richards, B. D. McKay and W. A. Richards, Collective Choice and Mutual Knowledge Structures, Adv. Complex Systems, 1 (1998) 221-236.
  95. E. A. Bender and E. R. Canfield and B. D. McKay, The asymptotic number of labeled graphs with n vertices, q edges, and no isolated vertices, J Combinatorial Theory, Series A, 80 (1997) 124-150. PDF
  96. B. D. McKay and S. P. Radziszowski, 2-(22,8,4) designs have no blocks of type 3, J. Combin. Math. Combin. Comput., 30 (1999) 251-253. dvi; ps.gz
  97. B. D. McKay and G. Brinkmann, Fast generation of some classes of planar graphs, Electron. Notes Disc. Math., 3 (1999) 28-31.
  98. R. E. L. Aldred, S. Bau, D. A. Holton and B. D. McKay, Cycles through 23 vertices in 3-connected cubic planar graphs, Graphs and Combinatorics, 15 (1999) 373-376. PDF.
  99. B. D. McKay, Isomorph-free exhaustive generation, J Algorithms, 26 (1998) 306-324. PDF with errata.
  100. B. D. McKay, M. Miller and J. Siran, A note on large graphs of diameter two and given maximum degree, J Combinatorial Theory, Series A, 74 (1998) 110-118. dvi; ps.gz
  101. B. D. McKay, W. Myrvold and J. Nadon, Fast backtracking principles applied to find new cages, 9th Annual ACM-SIAM Symposium on Discrete Algorithms, January 1998, 188-191. PDF.
  102. B. D. McKay and I. M. Wanless, Most Latin squares have many subsquares, J. Combinatorial Theory, Ser. A, 86 (1999) 323-347. ps.gz.
  103. B. D. McKay, D. Bar-Natan, M. Bar-Hillel and G. Kalai, Solving the Bible code puzzle, Statistical Science, 14 (1999) 150-173. dedicated web page.
  104. M. J. Wolf, S. Easteal, M. Kahn, B. D. McKay and L. S. Jermiin, TrExML: a maximum-likelihood approach for extensive tree-space exploration, Bioinformatics, 16 (2000) 383-394.
  105. R. E. L. Aldred and B. D. McKay, Graceful and harmonious labellings of small trees, ICA Bulletin, 23 (1998) 69-72. ps; PDF.
  106. R. E. L. Aldred, S. Bau, D. A. Holton and B. D. McKay, Nonhamiltonian 3-connected cubic planar graphs, SIAM J. Disc. Math., 13 (2000) 25-32. PDF.
  107. Z. Gao, B. D. McKay and X. Wang, Asymptotic enumeration of tournaments with a given score sequence containing a specified digraph, Random Structures and Algorithms, 16 (2000) 47-57. PDF.
  108. B. D. McKay, N. D. Megill and M. Pavičić, Algorithms for Greechie Diagrams, Internat. J. Theor. Phys., 39 (2000) 2393-2417. arXiv.
  109. B. D. McKay and E. Spence, Classification of regular two-graphs on 36 and 38 vertices, Australasian J. Combinatorics, 24 (2001) 293-300. PDF.
  110. S-H. Hong, B. D. McKay and P. Eades, Symmetric Drawings of Triconnected Planar Graphs, Thirteenth ACM-SIAM Symposium on Discrete Algorithms, San Fransisco, January 2002.
  111. M. Paredes, P. Gonzalez and B. D. McKay, Sobre un Tipo Especial de Torneos y una Clase de Métricas sobre Variedades Bandera (in Spanish), Primera Conferencia Iberoamericana de Matematica Computacional (Thomson Learning de Colombia, Bogota, 2001) 125-138.
  112. D. Richards, W. A. Richards and B. D. McKay, The probability of collective choice with shared knowledge structures, J. Math. Psychology, 46 (2002) 338-351.
  113. B. D. McKay, J. Morse and H. S. Wilf, The distributions of the entries of Young tableaux, J. Combinatorial Theory, Series B, 97 (2002) 117-128. arXiv.
  114. B. D. McKay, I. M. Wanless and N. C. Wormald, Asymptotic enumeration of graphs with a given bound on the maximum degree, Combinatorics, Probability and Computing, 11 (2002) 373-392. PDF.
  115. G. Brinkmann and B. D. McKay, Posets on up to 16 points, Order, 19 (2002) 147-179. PDF.
  116. G. Brinkmann, B. D. McKay and U. von Nathusius, Backtrack search and look-ahead for the construction of planar cubic graphs with restricted face sizes, MATCH, 48 (2003) 163-177.
  117. B. D. McKay and X. Wang, Asymptotic enumeration of 0-1 matrices with equal row sums and equal column sums, Linear Alg. Appl., 373 (2003) 273-288. doi:10.1016/S0024-3795(03)00506-8.
  118. B. D. McKay, E. M. Palmer, R. C. Read and R. W. Robinson, The asymptotic number of claw-free cubic graphs, Discrete Applied Math., 272 (2003) 107-118. PDF.
  119. B. D. McKay, K. Piwakowski and S. P. Radziszowski, Ramsey numbers for triangles versus almost-complete graphs, Ars Combinatoria, Ars Combinatoria, 73 (2004), 205-214. PDF.
  120. B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, H. S. Wilf, I. M. Wanless, Acyclic Digraphs and Eigenvalues of (0,1)-Matrices, J. Integer Sequences, 7 (2004) 5 pages. JIS.
  121. B. D. McKay, N. C. Wormald and B. Wysocka, Short cycles in random regular graphs, Elect. J. Combinatorics, 11, R66, 12 pages. E-JC home page.
  122. M. Pavičić, J.-P. Merlet, B. D. McKay and N. D. Megill, Kochen-Specker vectors, J. Phys. A: Math. Gen., 38 (2005) 1577-1592. arXiv.
  123. G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas and P. Wollan, Generation of simple quadrangulations of the sphere, Discrete Mathematics, 305 (2005) 33-54. PDF (corrected).
  124. B. D. McKay, A. Meynert and W. Myrvold, Small Latin squares, quasigroups and loops, J. Combinatorial Designs, 15 (2007) 98-119. PDF (corrected).
  125. G. Brinkmann and B. D. McKay, Counting unlabelled topologies and transitive relations, J. Integer Sequences, 8 (2005) 7 pages. JIS page.
  126. G. Brinkmann and B. D. McKay, Construction of planar triangulations with minimum degree 5, Discrete Mathematics 301 (2005) 147-163. PDF.
  127. B. D. McKay and I. M. Wanless, On the number of Latin squares, Annals of Combinatorics, 9 (2005) 335-344. PDF
  128. E. R. Canfield and B. D. McKay, Asymptotic enumeration of dense 0-1 matrices with equal row sums and equal column sums, Electronic J. Combin., 12 (2005) #R29. E-JC page.
  129. C. Greenhill, B. D. McKay and X. Wang, Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums, J. Combinatorial Theory, Ser. A, 113 (2006) 291-324. PDF
  130. S-H. Hong, B. D. McKay and P. Eades, A linear time algorithm for constructing maximally symmetric straight-line drawings of triconnected planar graphs, Disc. Comp. Geometry, 36 (2006) 283-311.
  131. D. Van Dyck, G. Brinkmann, V. Fack and B. D. McKay, To be or not to be Yutsis: algorithms for the decision problem, Computer Physics Communications, 173 (2005) 61-70. PDF
  132. P. Lieby, N. Barnes, and B. D. McKay, Topological repair on voxel-based quadrangular Meshes, in Mathematical Foundations of Computational Anatomy, MICCAI 2006 Workshop Proceedings, 2006, 146-155.
  133. V. Fack and B. D. McKay, A generalized switching method for combinatorial estimation, Australasian J. Combin., 39 (2007) 141-154. PDF.
  134. B. D. McKay, J. C. McLeod and I. M. Wanless, The number of transversals in a Latin square, Designs, Codes and Cryptography, 40 (2006) 269-284.
  135. E. R. Canfield, C. Greenhill and B. D. McKay, Asymptotic enumeration of dense 0-1 matrices with specified line sums, J. Combin. Th., Ser. A, 115 (2008) 32-66. arXiv.
  136. B. D. McKay and I. M. Wanless, A census of small latin hypercubes, SIAM J. Disc. Math., 22 (2008) 719-736.
  137. G. Brinkmann and B. D. McKay, Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem., 58 (2007) 323-357. PDF (expanded edition).
  138. C. S. Greenhill and B. D. McKay, Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums, Adv. Appl. Math., 41 (2008) 459-481. arXiv.
  139. R. E. L. Aldred, G. Brinkmann, V. Fack, B. D. McKay and D. Van Dyck, Graph structural properties of non-Yutsis graphs allowing fast recognition, Disc. Appl. Math., 157 (2009) 377-386.
  140. E. R. Canfield and B. D. McKay, The asymptotic volume of the Birkhoff polynomial, Online J. Anal. Comb., Issue 4 (2009) #2. PDF.
  141. M. Hasheminezhad, H. Fleischner and B. D. McKay, A universal set of growth operations for fullerenes, Chem. Phys. Lett., 464 (2008) 118-121.
  142. P. Lieby, B. D. McKay, J. C. McLeod and I. M. Wanless, Subgraphs of random k-edge-coloured k-regular graphs, Combin. Probab. Comput., 18 (2009) 533-549. PDF.
  143. C. S. Greenhill and B. D. McKay, Random dense bipartite graphs and directed graphs with specified degrees, Random Struct. Alg., 35 (2009) 222-249. arXiv.
  144. M. Hasheminezhad and B. D. McKay, Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4, Discussiones Mathematicae Graph Theory, 30 (2010) 123-136. PDF.
  145. M. Kobayashi, B. D. McKay, N. Mutoh, G. Nakamura, Black 1-factors and Dudeney sets, J. Combin. Math. Combin. Comput., 75 (2010) 167-174.
  146. G. Exoo, B. D. McKay, W. Myrvold, Computational determination of (3,11) and (4,7) cages. J. Disc. Alg., 9 (2011) 166-169. arXiv.
  147. M. Hasheminezhad, S. M. Hashemi and B. D. McKay, Rectangular-radial drawings of cubic plane graphs, J. Comput. Geom. Theory and Appl., 43 (2010) 767-780. PDF.
  148. E. R. Canfield, Z. Gao, C. S. Greenhill, B. D. McKay and R. W. Robinson, Asymptotic enumeration of correlation-immune boolean functions, Cryptography and Communications, 2 (2010) 111-126. arXiv.
  149. M. Hasheminezhad and B. D. McKay, Combinatorial estimates by the switching method, Contemporary Mathematics, 531 (2010) 209-221. PDF.
  150. M. Hasheminezhad, S. M. Hashemi and B. D. McKay, Spherical-rectangular drawings, Lecture Notes Comp. Sci., 5431 (2009) 129-140. PDF.
  151. M. Hasheminezhad, B. D. McKay and T. Reeves, Recursive generation of 5-regular planar graphs, Lecture Notes Comp. Sci., 5431 (2009) 345-356.
  152. E. R. Canfield and B. D. McKay, Asymptotic enumeration of integer matrices with large equal row and column sums, Combinatorica, 30 (2010) 655-680. arXiv
  153. B. D. McKay, Subgraphs of random graphs with specified degrees, Proceedings of the International Congress of Mathematicians, Hyderabad, 2010. PDF.
  154. B. D. McKay, Subgraphs of dense random graphs with specified degrees. Combinatorics, Probability and Computing, 20 (2011) 413-433. arXiv.
  155. M. Hasheminezhad, B. D. McKay and T. Reeves, Recursive generation of simple planar 5-regular graphs and pentangulations, J. Graph Algorithms Appl., 15 (2011) 417-436.
  156. M. Pavičić, B. D. McKay, N. D. Megill and K. Fresl, Graph approach to quantum systems, J. Math. Physics, 51 (2010) 102103 (31pp). arXiv.
  157. B. D. McKay and C. Greenhill, Counting loopy graphs with given degrees, Linear Alg. Appl., to appear. arXiv.
  158. G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discrete Math. Theor. Comput. Sci., 13 (2011) 69-80.
  159. G. Brinkmann, J. Goedgebeur and B. D. McKay, The smallest fullerene without a spiral, Chem. Phys. Lett., to appear.
  160. B. D. McKay, A note on the history of the four-colour conjecture, J. Graph Theory, 72 (2013) 361-363. arXiv.
  161. B. D. McKay and J. C. McLeod, Asymptotic enumeration of symmetric integer matrices with uniform row sums. J. Australian Math. Soc., 92 (2012) 367-384. arXiv.
  162. M. Kobayashi, B. D. McKay, N. Mutoh, G. Nakamura and C. Nara, 3-Perfect hamiltonian decomposition of the complete graph, Australasian J. Combin., 56 (2013) 219-224.
  163. G. Brinkmann, J. Goedgebeur and B. D. McKay, The generation of fullerenes, J. Chem. Inf. Modelling, 52 (2012) 2910-2918. arXiv.
  164. B. D. McKay, P. Schweitzer and P. Schweitzer, Competition numbers, quasi-line graphs and holes, SIAM J Disc. Math., 28 (2014) 77-91. arXiv.
  165. B. D. McKay and P. Schweitzer, Switching reconstruction of digraphs. J. Graph Theory, 76 (2014) 279-296. arXiv.
  166. B. D. McKay and A. Piperno, Practical Graph Isomorphism, II, J. Symbolic Comput., 60 (2014) 94-112. arXiv.
  167. B. D. McKay, I. M. Wanless and X. Zhang, The order of automorphisms of quasigroups, J. Combin. Designs, 23 (2015) 275-288.
  168. A. B. Carneiro, C. N. da Silva, B. D. McKay, A Faster Test for 4-Flow-Criticality in Snarks. In: VIII Latin-American Algorithms, Graphs and Optimization Symposium, 2015, Beberibe, Brazil. Electronic Notes in Discrete Mathematics, 50 (2015) 193-198.
  169. C. Greenhill and B. D. McKay, Asymptotic enumeration of sparse multigraphs with given degrees, SIAM J. Disc. Math., 27 (2013) 2064-2089. arXiv.
  170. R. E. L. Aldred, R. A. Bailey, B. D. McKay and I. M. Wanless, Circular designs balanced for neighbours at distances one and two, Biometrika, 101 (2014) 943-956. PDF.
  171. J. Goedgebeur and B. D. McKay, Recursive generation of IPR fullerenes, J. Math. Chem., 53 (2015) 1702-1724. arXiv.
  172. Goedgebeur and B. D. McKay, Fullerenes with distant pentagons, MATCH Commun. Math. Comput. Chem., 74 (2015) 659-672. arXiv.
  173. M. Jooyandeh, B. D. McKay, P. R. J. Östergård, V. H. Pettersson and C. T. Zamfirescu. Planar Hypohamiltonian Graphs on 40 Vertices, J. Graph Theory, 84 (2017) 121-133. arXiv.
  174. B. D. McKay and F. Skerman, Degree sequences of random digraphs and bipartite graphs. J. Combinatorics, 7 (2016) 21-49. arXiv.
  175. I. Isaev and B. D. McKay, On a bound of Hoeffding in the complex case, Electron. Comm. Prob., 21 (2016) #14, 1-7. arXiv.
  176. B. D. McKay, Hypohamiltonian planar cubic graphs with girth 5, J. Graph Theory, 85 (2017) 7-11.
  177. Z. Gao, B. D. McKay, R. Nazerasr and B. Stevens, Bipartite edge partitions and the former Alon-Saks-Seymour Conjecture, Australasian J. Combin., 66 (2016) 211-228. PDF.
  178. N. Francetić, S. Herke, B. D. McKay and I. M Wanless, On Ryser's conjecture for linear intersecting multipartite hypergraphs, Europ. J. Combin., 61 (2017) 91-105. arXiv.
  179. C. Greenhill, M. Isaev, M. Kwan and B. D. McKay, The average number of spanning trees in sparse graphs with given degrees. Europ. J. Combin., 63 (2017) 6-25. arXiv.
  180. B. D. McKay, A class of Ramsey-extremal hypergraphs. Trans. Combinatorics, 6 (2017) 37-43. arXiv.
  181. M. Isaev and B. D. McKay, Complex martingales and asymptotic enumeration. Random Structures and Algorithms, 52 (2018) 617-661. arXiv.
  182. V. Angeltveit and B. D. McKay, R(5,5) ≤ 48, J. Graph Theory, 89 (2018) 5-13. arXiv.
  183. N. Alon, S. M. Cioaba, B. D. Gilbet, J. H. Keelen and B. D. McKay, Addressing Johnson graphs, complete multipatite graphs, odd cycles and other graphs, J. Experimental Math. doi:10.1080/10586458.2018.1542643
  184. B. D. McKay and J. C. McLeod, The r-switching-stable graphs, Discrete Appl. Math., 266 (2019) 16-29; doi:10.1016/j.dam.2018.12.01.
  185. M. Hasheminezhad and B. D. McKay, Asymptotic enumeration of non-uniform linear hypergraphs, Discussiones Math. Graph Th., doi:10.7151/dmgt.2246
  186. M. Isaev, T. Iyer and B. D McKay, Asymptotic enumeration of orientations of a graph as a function of the out-degree sequence, Electron. J. Combin., 27 (2020) #P1.26. E-JC.
  187. B. D. McKay and Fang Tian, Asymptotic enumeration of linear hypergraphs with given number of vertices and edges, Advances Appl. Math, 115 (2020). arXiv. 10.1016/j.aam.2020.102000.
  188. M. Farhan, Qing Wang, Yu Lin, B. D. McKay, A highly scalable labelling approach for exact distance queries in complex networks. 22nd International Conference on Extending Database Technology (EDBT), 2019}.
  189. P. Gao, M. Isaev and B. D. McKay, Sandwiching random regular graphs between binomial random graphs, SIAM Conference on Discrete Algorithms (SODA 2020).
  190. S. Kiefer and B. D. McKay, The iteration number of colour refinement, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), arXiv. PDF.
  191. C. S. Greenhill, M. Isaev and B. D. McKay, Subgraph counts for dense random graphs with specified degrees, Combin. Prob. Comput., 30 (2021) 460-497. doi:10.1017/S0963548320000498.
  192. G. Brinkmann, J. Goedgebeur and B. D. McKay, The minimality of the Georges-Kelmans graph. Math. Computation, 91 (2022) 1483-1500. arXiv.
  193. M. Farhan, Qing Wang, Yu Lin, B. D. McKay, Fast fully dynamic labelling for distance queries, The VLDB Journal, 31 (2021) 483-506.
  194. B. D. McKay and I. M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Designs, 30 (2022) 105-130 doi:10.1002/jcd.21814.
  195. B. D. McKay, C. Steinbeck and M. A. Yirik, Surge - A Fast Open-Source Chemical Graph Generator, Journal of Cheminformatics, 13 (2022) #24. ChemRxiv.
  196. B. D. McKay, Reconstruction of small graphs and digraphs. Austral. J. Combin, 83 (2022) 448-457. PDF.
  197. C. Greenhill, M. Isaev, T. Makai and B. D. McKay, Degree sequences of sufficiently dense random uniform hypergraphs. Combin. Prob. Comput., online 2022. arXiv.
  198. Pu Gao, M. Isaev and B. D. McKay, Sandwiching dense random regular graphs between binomial random graphs. Probab. Th. Related Fields, online 2022. PDF.
  199. B. D. McKay and T. Peters, Paths through equally spaced points on a circle, J. Integer Sequences, 25 (2022), #22.7.4. PDF
  200. M. Hasheminezhad and B. D. McKay, Factorisation of the complete graph into spanning regular factors, Advances Appl. Math., to appear (2023). arXiv.
  201. M. Hasheminezhad and B. D. McKay, Factorisation of the complete bipartite graph into spanning semiregular factors, Annals of Combinatorics, to appear (2023). arXiv.

Articles submitted for publication.

Technical Reports, other articles, etc.

  1. B. D. McKay, A macro menagerie, TUGboat, 2 (1981) 46-49. PDF
  2. B. D. McKay, Eulerian circuits in Kn, Combinatorics (newsletter of the Combinatorial Math. Soc. of Australasia), 4 (1982) 5-6.
  3. B. D. McKay, nauty User's Guide, Tech. Rpt. TR-CS-84-05, Dept. Computer Science, Austral. Nat. Univ. (1984).
  4. B. D. McKay, nauty User's Guide (version 1.2), Tech. Rpt. TR-CS-87-03, Dept. Computer Science, Austral. Nat. Univ. (1987).
  5. B. D. McKay, nauty User's Guide (version 1.5), Tech. Rpt. TR-CS-90-02, Dept. Computer Science, Austral. Nat. Univ. (1990).
  6. R. J. Faudree and B. D. McKay, The number of walks of length a power of three in a graph, preprint (1980).
  7. J. C. Lagarias, J. E. Mazo, B. D. McKay and L. A. Shepp, An inequality for walks in a graph, Problem 83-15 and solution by proposers, Siam Review, 26 (1984) 580-582.
  8. K. Malysiak and B. D. McKay, Combinatorial optimisation on the AP1000, Proc. Second Fujitsu-ANU CAP Workshop, Australian National University November 1991.
  9. B. D. McKay, autoson - a distributed batch system for UNIX workstation networks (version 1.3), Tech. Rpt. TR-CS-96-03, Dept. Computer Science, Austral. Nat. Univ. (1996).
  10. B. D. McKay, Knight's tours of an 8x8 chessboard, Tech. Rpt. TR-CS-97-03, Dept. Computer Science, Austral. Nat. Univ. (1997). PDF.
  11. A. Tridgell, R. Brent and B. D. McKay, Parallel integer sorting, Tech. Rpt. TR-CS-97-10, Dept. Computer Science, Austral. Nat. Univ. (1997).
  12. B. D. McKay, The Internet diary of the man who cracked the "Bible Code", Yahoo Internet Life, 3, No. 8, August 1997.
  13. M. Bar-Hillel, D. Bar-Natan and B. D. McKay, There are codes in War and Peace too, Galileo, 25, Nov-Dec 1997, 52-57 (in Hebrew).
  14. D. Bar-Natan and B. D. McKay, Equidistant Letter Sequences in Tolstoy's "War and Peace", preprint 1997. www.
  15. D. Bar-Natan, B. D. McKay and S. Sternberg, On the Witztum-Rips-Rosenberg sample of nations, preprint 1998. www.
  16. M. Bar-Hillel, D. Bar-Natan and B. D. McKay, The Torah Codes: Puzzle and Solution, Chance, 11 (1998) 13-19.
  17. M. Bar-Hillel, D. Bar-Natan and B. D. McKay, Il codice segreto della Bibbia (Italian), KOS, 163 new series (1999), 56-64.
  18. B. D. McKay, A. Meynert and W. Myrvold, Counting small Latin squares, in Groups and Graphs, Proceedings of the European Women in Mathematics, International Workshop on Groups and Graphs, Varna, Bulgaria, 2002, 670-672.
  19. B. D. McKay, Confessions of a Codes Buster, The Skeptic, Spring 2003, 12-15.
  20. B. D. McKay and G. F. Royle, There are 2834 spreads of lines in PG(3,8), arXiv.

Substantial works edited.

  1. Proceedings of the Second International Conference on Combinatorial Mathematics and Computing, (Canberra, Aug. 24-28, 1987), Ars Combinatoria, volumes 26-A and 26-B.
  2. Special issue in honour of Ralph G. Stanton (with J. Seberry and S. Vanstone), Discrete Mathematics 92, 1-3, 1990; also printed separately as Selected Papers in Combinatorics, North-Holland (Amsterdam, 1992).

Book reviews.

  1. The Peterson Graph (D. Holton and J. Sheehan; Australian Lecture Notes Series, Number 7, Cambridge University Press, Cambridge, 1993), Australian Math. Soc. Gazette, 22 (1995) 92-93.

Please feel free to ask for additional electronic editions of papers to be added here.

Back to my home page.