Peter Bradshaw

For a given $\epsilon > 0$, we say that a graph $G$ is $\epsilon$-flexibly $k$-choosable if the following holds: for any assignment $L$ of lists of size $k$ on $V(G)$, if a preferred color is requested at any set $R$ of vertices, then at least $...

Abstract: Given a family G of graphs on a common vertex set X, we say that G is rainbow connected if for every vertex pair u, v ∈ X, there exists a path from u to v that uses at most one edge from each graph of G. We consider the case that G contains...

We explore classes of graphs on which a large number of pursuers are required to capture an evader. We give a lower bound for the cop number of graphs of high girth that improves a result of P. Frankl. We also consider lower bounds for the cop number...

We explore graphs of high cop number. We give new lower bounds for cop number of graphs of high girth. We also present a new class of undirected graphs with cop number $(1-o(1)) \sqrt{n/2}$ and a class of directed graphs with cop number $(1-o(1))...