The problem of routing and wavelength assignment in all-optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths, f...
We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
The Grundy number of a graph G, denoted by (G), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm...
This paper introduces a new strategy for playing the marking game on graphs. Using this strategy, we prove that if G is a planar graph, then the game colouring number of G, and he...