We consider the following question: how large does n have to be to guarantee that in any two-colouring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In th...
Abstract. We answer two questions of Zhu on circular choosability of graphs. We show that the circular list chromatic number of an even cycle is equal to 2 and give an example of a...
We determine necessary and sufficient conditions for a complete multipartite graph to admit a set of 1-factors whose union is the whole graph and, when these conditions are satisf...
: A (g, f )-factor of a graph is a subset F of E such that for all v V, g(v) degF(v) f(v). Lovasz gave a necessary and sufficient condition for the existence of a (g, f )-factor...