Let G be a planar graph. The vertex face total chromatic number ,y13(G) of G is the least number of colors assigned to V(G) U F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for
Recent results on the total chromatic number
β Scribed by A.J.W. Hilton
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 626 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Hilton, A.J.W., Recent results on the total chromatic number, Discrete Mathematics 111 (1993) 323-331.
We give a survey of various recent results concerning the total chromatic number of simple graphs.
π SIMILAR VOLUMES
The mean chromatic number of a graph is a measure of the expected performance of the greedy vertex-colouring algorithm when each ordering of the vertices is equally likely. Some results on the value of the mean chromatic number and its asymptotic behaviour are presented.
In this paper, we shall first prove that for a Halin graph G, 4 Β°xT (G) Β°6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff
## Abstract In this paper we discuss some estimates for upper bounds on a number of chromatic parameters of a multigraph. In particular, we show that the total chromatic number for an __n__βorder multigraph exceeds the chromatic index by the smallest __t__ such that __t__! > __n__.
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.