Dr Brendan McKay

BSc (Hons), MSc, PhD (Melbourne, 1980)

Professor

ANU College of Engineering, Computing and Cybernetics

E: bdm@cs.anu.edu.au

T: +61 2 6125 3845

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Areas of expertise

Probability Theory 010404
Applied Discrete Mathematics 080202
Approximation Theory And Asymptotic Methods 010201
Mathematical Software 080204
Numerical Analysis 010301
Algebra And Number Theory 010101
Analysis Of Algorithms And Complexity 080201
Combinatorics And Discrete Mathematics (Excl. Physical Combinatorics) 010104
Numerical And Computational Mathematics 0103
Theoretical And Computational Chemistry 0307
Computation Theory And Mathematics 0802

Publications

Alon, N, Cioaba, S, Gilbert, B et al. 2021, 'Addressing Johnson Graphs, Complete Multipartite Graphs, Odd Cycles, and Random Graphs', Experimental Mathematics, vol. 30, no. 3, pp. 372-382.
Farhan, M, Wang, Q, Lin, Y et al. 2021, 'Fast fully dynamic labelling for distance queries', VLDB Journal, The, vol. 31, pp. 483ÃÂ¢Ã¢Â¬Ã¢506.
Greenhill, C, Isaev, M & McKay, B 2021, 'Subgraph counts for dense random graphs with specified degrees', Combinatorics Probability and Computing, vol. 30, no. 3, pp. 460-497.
McKay, B & Tian, F 2020, 'Asymptotic enumeration of linear hypergraphs with given number of vertices and edges', Advances in Applied Mathematics, vol. 115.
Isaev, M, Iyer, T & McKay, B 2020, 'Asymptotic enumeration of orientations of a graph as a function of the out-degree sequence', Electronic Journal of Combinatorics, vol. 27, no. 1.
Hasheminezhad, M & McKay, B 2019, 'Asymptotic Enumeration of Non-Uniform Linear Hypergraphs', Discussiones Mathematicae - Graph Theory, vol. 42, no. 1, pp. 219-230.
McLeod, J, McKay, B & Faller, B 2019, 'The r-switching-stable graphs', Discrete Applied Mathematics, vol. 266, pp. 16-29.
Isaev, M & McKay, B 2018, 'Complex martingales and asymptotic enumeration', Random Structures and Algorithms, vol. 52, no. 4, pp. 617-661pp.
Angeltveit, V & McKay, B 2018, 'R(5,5)≤48', Journal of Graph Theory, vol. 89, no. 1, pp. 5-13pp.
McKay, B 2017, 'Hypohamiltonian Planar Cubic Graphs with Girth 5', Journal of Graph Theory, vol. 85, no. 1, pp. 7-11.
Jooyandeh, M, McKay, B, Ostergard, P et al 2017, 'Planar Hypohamiltonian Graphs on 40 Vertices', Journal of Graph Theory, vol. 84, no. 2, pp. 121-133.
Greenhill, C, Isaev, M, Kwan, M et al 2017, 'The average number of spanning trees in sparse graphs with given degrees', European Journal of Combinatorics, vol. 63, pp. 6-25pp.
McKay, B 2017, 'A class of Ramsey-extremal hypergraphs', Transactions on Combinatorics, vol. 6, no. 3, pp. 37-43.
Francetic, N, Herke, S, McKay, B et al 2017, 'On Ryser's conjecture for linear intersecting multipartite hypergraphs', European Journal of Combinatorics, vol. 61, pp. 91-105pp.
McKay, B & Skerman, F 2016, 'Degree sequences of random digraphs and bipartite graphs', Journal of Combinatorics, vol. 7, no. 1, pp. 21-49.
Gao, Z, McKay, B, Naserasr, R et al 2016, 'Bipartite edge partitions and the former Alon-Saks-Seymour conjecture', Australasian Journal of Combinatorics, vol. 66, no. 2, pp. 211-228.
Isaev, M & McKay, B 2016, 'On a bound of Hoeffding in the complex case', Electronic Communications in Probability, vol. 21, pp. 1-7.
McKay, B, Wanless, I & Zhang, X 2015, 'The order of automorphisms of quasigroups', Journal of Combinatorial Designs, vol. 23, no. 7, pp. 275-288.
Goedgebeur, J & McKay, B 2015, 'Fullerenes with distant pentagons', MATCH - Communications in Mathematical and in Computer Chemistry, vol. 74, no. 3, pp. 659-672.
Carneiro, A, da Silva, C & McKay, B 2015, 'A Faster Test for 4-Flow-Criticality in Snarks', Electronic Notes in Discrete Mathematics, vol. 50, pp. 193-198.
Goedgebeur, J & McKay, B 2015, 'Recursive generation of IPR fullerenes', Journal of Mathematical Chemistry, vol. 53, no. 8, pp. 1702-1724.
McKay, B 2014, 'Graph Isomorphism', in Jonathan L. Gross, Jay Yellen, Ping Zhang (ed.), Handbook of Graph Theory, Second Edition, CRC Press, Boca Raton, FL, USA, pp. 68-76pp.
McKay, B, Schweitzer, P & Schweitzer, P 2014, 'Competition numbers, quasi-line graphs, and holes', SIAM Journal on Discrete Mathematics, vol. 28, no. 1, pp. 77-91.
Aldred, R, Bailey, R, McKay, B et al 2014, 'Circular designs balanced for neighbours at distances one and two', Biometrika, vol. 101, no. 4, pp. 943-956.
McKay, B 2014, 'Section 2.2 Graph Isomorphism', in Jonathan L. Gross, Jay Yellen, Ping Zhang (ed.), Handbook of Graph Theory, Second Edition, CRC Press, Boca Raton, FL, USA, pp. 68-76.
McKay, B & Schweitzer, P 2014, 'Switching Reconstruction of Digraphs', Journal of Graph Theory, vol. 76, no. 4, pp. 279-296.
McKay, B & Piperno, A 2014, 'Practical graph isomorphism, II', Journal of Symbolic Computation, vol. 60, pp. 94-112.
McKay, B & Royle, G 2014, 'There are 2834 spreads of lines in PG(3, 8)', arXiv (e-archive for Pre-prints, author submits), vol. 1404.1643v1.
Greenhill, C & McKay, B 2013, 'Asymptotic Enumeration of Sparse Multigraphs with Given Degrees', SIAM Journal on Discrete Mathematics, vol. 27, no. 4, pp. 2064-2089.
Kobayashi, M, McKay, B, Mutoh, N et al 2013, '3-perfect hamiltonian decomposition of the complete graph', Australasian Journal of Combinatorics, vol. 56, pp. 219-224.
McKay, B 2013, 'A Note on the History of the Four-Colour Conjecture', Journal of Graph Theory, vol. 72, no. 3, pp. 361-363.
Brinkmann, G, Goedgebeur, J & McKay, B 2012, 'The smallest fullerene without a spiral', Chemical Physics Letters, vol. 522, pp. 54-55.
Brinkmann, G, Goedgebeur, J & McKay, B 2012, 'The Generation of Fullerenes', Journal of Chemical Information and Modeling, vol. 52, no. 11, pp. 2910-2918.
McKay, B & McLeod, J 2012, 'Asymptotic enumeration of symmetric integer matrices with uniform row sums', Journal of the Australian Mathematical Society, vol. 92, no. 3, pp. 367-384.
Greenhill, C & McKay, B 2012, 'Counting loopy graphs with given degrees', Linear Algebra and its Applications, vol. 436, no. 4, pp. 901-926.
McKay, B 2011, 'Subgraphs of Dense Random Graphs with Specified Degrees', Combinatorics Probability and Computing, vol. 20, no. 3, pp. 413-433.
Exoo, G, McKay, B, Myrvold, W et al 2011, 'Computational determination of (3, 11) and (4, 7) cages', Journal of Discrete Algorithms (Amsterdam), vol. 9, no. 2, pp. 166-169.
Hasheminezhad, M, McKay, B & Reeves, T 2011, 'Recursive generation of simple planar 5-regular graphs and pentangulations', Journal of Graph Algorithms and Applications, vol. 15, no. 3, pp. 417-436.
Brinkmann, G, Goedgebeur, J & McKay, B 2011, 'Generation of Cubic graphs##', Discrete Mathematics & Theoretical Computer Science, vol. 13, no. 2, pp. 69-80.
Pavicic, M, McKay, B, Megill, N et al 2010, 'Graph approach to quantum systems', Journal of Mathematical Physics, vol. 51, no. 10, pp. 102103-1 - 102103-31.
Kobayashi, M, McKay, B, Mutoh, N et al 2010, 'Black 1-factors and Dudeney sets', Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC), vol. 75, pp. 167-174.
Hasheminezhad, M & McKay, B 2010, 'Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4', Discussiones Mathematicae - Graph Theory, vol. 30, no. 1, pp. 123-136.
Canfield, E, Gao, Z, Greenhill, C et al 2010, 'Asymptotic enumeration of correlation-immune boolean functions', Cryptography and Communications, vol. 2, no. 1, pp. 111-126.
Hasheminezhad, M & McKay, B 2010, 'Combinatorial estimates by the switching method', Contemporary Mathematics.
McKay, B 2010, 'Subgraphs of random graphs with specified degrees', International Congress of Mathematicians 2010, ICM 2010, Conference Organising Committee, Hyderabad, pp. 2489-2501.
Canfield, E & McKay, B 2010, 'Asymptotic Enumeration Of Integer Matrices With Large Equal Row And Column Sums', Combinatorica, vol. 30, no. 6, pp. 655-680.
Hasheminezhad, M, Hashemi, S, McKay, B et al 2010, 'Rectangular-radial drawings of cubic plane graphs', Computational Geometry: Theory and Applications, vol. 43, no. 9, pp. 767-780.
Lieby, P, McKay, B, McLeod, J et al 2009, 'Subgraphs of Random k-Edge-Coloured k-Regular Graphs', Combinatorics Probability and Computing, vol. 18, pp. 533-549.
McKay, B & Canfield, E 2009, 'The asymptotic volume of the Birkhoff polytope', Online Journal of Analytic Combinatorics, vol. 1, no. 4, p. 4.
Greenhill, C & McKay, B 2009, 'Random Dense Bipartite Graphs and Directed Graphs with Specified Degrees', Random Structures and Algorithms, vol. 35, no. 2, pp. 137-270.
Hasheminezhad, M, McKay, B & Reeves, T 2009, 'Recursive Generation of 5-Regular Planar Graphs', in Sandip Das & Ryuhei Uehara (ed.), WALCOM: Algorithms and Computation, Springer, New York, pp. 129-140.
Hasheminezhad, M, Hashemi, S & McKay, B 2009, 'Spherical-Rectangular Drawings', in Sandip Das & Ryuhei Uehara (ed.), WALCOM: Algorithms and Computation, Springer, New York, pp. 345-356.
Greenhill, C & McKay, B 2008, 'Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums', Advances in Applied Mathematics, vol. 41, no. 4, pp. 459-481.
McKay, B & Wanless, I 2008, 'A Census of Small Latin Hypercubes', SIAM Journal on Discrete Mathematics, vol. 22, no. 2, pp. 719-736.
Aldred, R, Van Dyck, D, Brinkmann, G et al 2008, 'Graph Structural Properties of Non-Yutsis Graphs Allowing Fast Recognition', Discrete Applied Mathematics, vol. 157, no. 2, pp. 377-386.
Hasheminezhad, M, Fleischner, H & McKay, B 2008, 'A universal set of growth operations for fullerenes', Chemical Physics Letters, vol. 464, pp. 118-121.
Canfield, E, Greenhill, C & McKay, B 2008, 'Asymptotic enumeration of dense 0-1 matrices with specified line sums', Journal of Combinatorial Theory Series A, vol. 115, pp. 32-66.
McKay, B 2008, 'Graph Isomorphism', in Ming-Yang Kao (ed.), Encyclopedia of Algorithms, Springer, New York, pp. 373-376.
McKay, B, Meynert, A & Myrvold, W 2007, 'Small Latin Squares, Quasigroups and Loops', Journal of Combinatorial Designs, vol. 15, no. 2, pp. 98-119.
Brinkmann, G & McKay, B 2007, 'Fast generation of planar graphs', MATCH - Communications in Mathematical and in Computer Chemistry, vol. 58, no. 2, pp. 323-357.
Fack, V & McKay, B 2007, 'A generalized switching method for combinatorial estimation', Australasian Journal of Combinatorics, vol. 39, pp. 141-154.
Lieby, P, Barnes, N & McKay, B 2006, 'Topological Repair on Voxel-Based Quadrangular Meshes', Mathematical Foundations of Computational Anatomy Conference (MFCA 2006), ed. X Pennec, S Joshi, Conference Organising Committee, Copenhagen Denmark, pp. 146-155.
Hong, S, McKay, B & Eades, P 2006, 'A linear time algorithm for constructing maximally symetric straight line drawings of triconnected planar graphs', Discrete and Computational Geometry, vol. 36, pp. 283-311.
Greenhill, C, McKay, B & Wang, X 2006, 'Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums', Journal of Combinatorial Theory Series A, vol. 113, pp. 291-324.
McKay, B, McLeod, J & Wanless, I 2006, 'The number of transversals in a latin square', Designs, Codes and Cryptography, vol. 40, pp. 269-284.
Brinkmann, G & McKay, B 2005, 'Construction of planar triangulations with minimum degree 5', Discrete Mathematics, vol. 301, pp. 147-163.
Pavicic, M, Merlet, J, McKay, B et al 2005, 'Kochen-Specker vectors', Journal of Physics A: Mathematical and General, vol. 38, pp. 1577-1592.
Van Dyck, D, Brinkmann, G, Fack, V et al 2005, 'To be or not to be Yutsis: Algorithms for the decision problem', Computer Physics Communications, vol. 173, pp. 61-70.
Brinkmann, G, Greenberg, S, Greenhill, C et al 2005, 'Generation of simple quadrangulations of the sphere', Discrete Mathematics, vol. 305, pp. 33-54.
McKay, B & Wanless, I 2005, 'On the Number of Latin Squares', Annals of Combinatorics, vol. 9, pp. 335-344.
Canfield, E & McKay, B 2005, 'Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums', Journal of Combinatorics, vol. 12, pp. R29.
Brinkmann, G & McKay, B 2005, 'Counting Unlabelled Topologies and Transitive Relations', Journal of Integer Sequences, vol. 8, pp. 05.2.1.
McKay, B, Oggier, F, Royle, G et al 2004, 'Acyclic Digraphs and Eigenvalues of O,1 Matrices', Journal of Integer Sequences, vol. 7, pp. 1-5.
McKay, B, Wormald, N & Wysocka, B 2004, 'Short cycles in random regular graphs', Journal of Combinatorics, vol. 11, no. 1 - R66, pp. 1-12.
McKay, B, Piwakowski, K & Radziszowski, S 2004, 'Ramsey numbers for triangles versus almost-complete graphs', Ars Combinatoria, vol. 73, pp. 205-214.
McKay, B, Palmer, E, Read, R et al 2003, 'The asymptotic number of claw-free cubic graphs', Discrete Mathematics, vol. 272, pp. 107-118.
Brinkmann, G & McKay, B 2003, 'Backtrack search and look-ahead for the construction of planar cubic graphs with restricted face sizes', MATCH - Communications in Mathematical and in Computer Chemistry, vol. 48, pp. 163-177.
McKay, B & Wang, X 2003, 'Asymptotic enumeration of 0 - 1 matrices with equal row sums and equal column sums', Linear Algebra and its Applications, vol. 373, pp. 273-287.
McKay, B, Wanless, I & Wormald, N 2002, 'Asymptotic enumeration of graphs with a given bound on the maximum degree', Combinatorics Probability and Computing, vol. 11, pp. 373-392.
Wolf, M, Easteal, S, Kahn, M et al. 2000, 'TrExML: a maximum-likelihood approach for extensive tree-space exploration', Bioinformatics, vol. 16, no. 4, pp. 383-394.
Aldred, R, Baudin, S, Holton, D et al 1999, 'Cycles Through 23 Vertices in 3-Connected Cubic Planar Graphs', Graphs and Combinatorics, vol. 15, pp. 373 - 376.
McKay, B & Wanless, I 1999, 'Most Latin Squares Have Many Subsquares', Journal of Combinatorial Theory Series A, vol. 86, pp. 323-347.
McKay, B, Bar-Natan, D, Bar-Hillel, M et al 1999, 'Solving the Bible Code Puzzle', Statistical Science, vol. 14, no. 2, pp. 149-173.
McKay, B & Robinson, R 1998, 'Asymptotic Enumeration of Eulerian circuits in the Complete Graph', Combinatorics Probability and Computing.

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Updated: 03 July 2024 / Responsible Officer: Director (Research Services Division) / Page Contact: Researchers