Dr Brendan McKay
BSc (Hons), MSc, PhD (Melbourne, 1980)
Professor
ANU College of Engineering, Computing and Cybernetics
T:
+61 2 6125 3845
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. 483ââ¬â506.
- 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.