Peter J. Cameron

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math.CO2025

Hall's marriage theorem

Peter J. Cameron

In 1935, Philip Hall published what is often referred to as ``Hall's marriage theorem'' in a short paper (P.~Hall, On Representatives of Subsets, \textit{J. Lond. Math. Soc.} (1) \…

math.CO2024

Simplicial complexes defined on groups

Peter J. Cameron

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes…

math.CO2024

EPPA numbers of graphs

David Bradley-Williams, Peter J. Cameron, Jan HubiÄka +1

If $G$ is a graph, $A$ and $B$ its induced subgraphs, and $f : A \to B$ an isomorphism, we say that $f$ is a \emph{partial automorphism} of $G$ . In 1992, Hrushovski proved that…