Delay Colourings of Cubic Graphs

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.

On parcimonious edge-colouring of graphs with maximum degree three

In a graph G of maximum degree ∆ let γ denote the largest fraction of edges that can be ∆ edge-coloured. Albertson and Haas showed that γ ≥ 13 15 when G is cubic . We show here that this result can be extended to graphs with maximum degree 3 with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for whic...

Workshop Cycles and Colourings 2006

s 1 van Aardt S. Maximal nontraceable oriented graphs . . . . . . . . . . 1 Bača M. Total labelings of graphs . . . . . . . . . . . . . . . . . . . . 1 Bacsó G. Elementary bipartite graphs and unique colorability . . . . . 1 Borowiecki M. On F -decompositions of graphs . . . . . . . . . . . . . 2 Bujtás Cs. Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees . . . . . . . . . . ....