The total chromatic number XT(G) of a graph G is the least number of colours needed to colour the edges and vertices of G so that no incident or adjacent elements receive the same colour. This paper shows that if G is odd order and regular of degree d > [(&? -1)/6]1 V(G)/, then a necessary and suffi
The total chromatic number of regular graphs of high degree
โ Scribed by DeZheng Xie; WanNian Yang
- Book ID
- 107347878
- Publisher
- SP Science China Press
- Year
- 2009
- Tongue
- English
- Weight
- 309 KB
- Volume
- 52
- Category
- Article
- ISSN
- 1674-7283
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Hilton, A.J.W. and H.R. Hind, The total chromatic number ofgraphs having large maximum degree, Discrete Mathematics 117 (1993) 127-140. The total colouring conjecture is shown to be correct for those graphs G having d(G)>21 V(G)I.
We show that a regular graph G of order at least 6 whose complement c is bipartite has total chromatic number d(G) + 1 if and only if (i) G is not a complete graph, and (ii) G#K when n is even. As an aid in"';he proof of this, we also show that , for n>4, if the edges of a Hamiltonian path of Kzn a
## Abstract In this article we prove that the total chromatic number of a planar graph with maximum degree 10 is 11. ยฉ 2006 Wiley Periodicals, Inc. J Graph Theory 54: 91โ102, 2007