5 papers
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…
The random -SAT Gibbs uniqueness threshold revisited
Arnab Chatterjee, Amin Coja-Oghlan, Catherine Greenhill +4
We prove that for any for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of rand…
Enumeration of dihypergraphs with specified degrees and edge types
Catherine Greenhill, Tamás Makai
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are usefu…
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…
Asymptotic enumeration of correlation-immune boolean functions
E. Rodney Canfield, Zhicheng Gao, Catherine Greenhill +2
A boolean function of boolean variables is {correlation-immune} of order if the function value is uncorrelated with the values of any of the arguments. Such functions a…