The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer µ0(g), the smallest number of v...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...
The chromatic capacity of a graph G; CAP (G) ; is the largest integer k such that there is a k-colouring of the edges of G such that when the vertices of G are coloured with the s...
In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere Sd in such a way that two vertices joined by an edge have distance more than √ 3 (i...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...