## Abstract In this article we prove that the total chromatic number of a planar graph with maximum degree 10 is 11. Β© 2006 Wiley Periodicals, Inc. J Graph Theory 54: 91β102, 2007
A note on the total chromatic number of Halin graphs with maximum degree 4
β Scribed by Zhongfu Zhang; Linzhong Liu; Jianfang Wang; Hongxiang Li
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 210 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we prove that XT(G) = 5 for any Halin graph G with A(G) = 4, where A(G) and XT(G) denote the maximal degree and the total chromatic number of G, respectively.
π 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.
The result announced in the title is proved. A new proof of the total 6-colorability of any multigraph with maximum degree 4 is also given.
## Abstract Let Ξ»(__G__) be the lineβdistinguishing chromatic number and __x__β²(__G__) the chromatic index of a graph __G__. We prove the relation Ξ»(__G__) β₯ __x__β²(__G__), conjectured by Harary and Plantholt. Β© 1993 John Wiley & Sons, Inc.