Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that -----(u)(v) is an arc in H whenever...
Suppose that n > (log k)ck , where c is a fixed positive constant. We prove that no matter how the edges of Kn are colored with k colors, there is a copy of K4 whose edges rece...
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...