Wilson-Schreiber Colourings of Cubic Graphs

Distance-regular graphs, MH-colourings and MLD-colourings

It is shown that the only bipartite distance regular graphs of diameter 3 which are MLDcolourable are the incidence graphs of complementary Hadamard designs.

Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms

Kempe Equivalence of Colourings of Cubic Graphs

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kemp...

Total and fractional total colourings of circulant graphs

In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.

Delay Colourings of Cubic Graphs

In this note we prove the conjecture of Wilfong, Haxell and Winkler (2001) that every bipartite multigraph with integer edge delays admits an edge colouring with d + 1 colours in the special case where d = 3. A connection to the Brualdi-RyserStein conjecture is discussed.