Brendan D. McKay

activity

20062026

collaborators

6 papers

math.CO2026

Ramsey numbers for regular induced subgraphs

Paul W. Dyson, Brendan D. McKay

A problem proposed by Erdős, Fajtlowicz and Staton asks for the smallest $n$ for which every graph on $n$ vertices contains a regular induced subgraph of order at least $k$ . A vari…

math.CO2026

Asymptotic enumeration of constrained bipartite, directed and oriented graphs by degree sequence

Catherine Greenhill, Mahdieh Hasheminezhad, Isaiah Iliffe +1

In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This ena…

math.CO2025

Subgraphs in random graphs with specified degrees and forbidden edges

John Larkin, Brendan D. McKay, Fang Tian

Let $G$ be a uniformly chosen simple (labelled) random graph with given degree sequence $d$ and let $X, Y, L$ be edge-disjoint graphs on the same vertex set as $G$ . We i…

math.CO2013

Asymptotic enumeration of sparse multigraphs with given degrees

Catherine Greenhill, Brendan D McKay

Let J and J* be subsets of Z+ such that 0,1\in J and 0\in J*. For infinitely many n, let k=(k_1,..., k_n) be a vector of nonnegative integers whose sum M is even. We find an asympt…

math.CO2009

Asymptotic enumeration of correlation-immune boolean functions

E. Rodney Canfield, Zhicheng Gao, Catherine Greenhill +2

A boolean function of $n$ boolean variables is {correlation-immune} of order $k$ if the function value is uncorrelated with the values of any $k$ of the arguments. Such functions a…

math.CO2006

Asymptotic enumeration of dense 0-1 matrices with specified line sums

E. Rodney Canfield, Catherine Greenhill, Brendan D. McKay

Let S=(s_1,s_2,..., s_m) and T = (t_1,t_2,..., t_n) be vectors of non-negative integers with sum_{i=1}^{m} s_i = sum_{j=1}^n t_j. Let B(S,T) be the number of m*n matrices over {0,1…