In this paper, we give sufficient conditions for simple graphs to be class 1. These conditions mainly depend on the edge-connectivity, maximum degree and the number of vertices of maximum degree of a graph. Using these conditions, we can extend various results of Chetwynd and Hilton, and Niessen and
The chromatic index of graphs with large maximum degree
โ Scribed by Michael J. Plantholt
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 508 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
Vizing's Theorem, any graph G has chromatic index equal either to its maximum degree A(G) or A(G) + 1. A simple method is given for determining exactly the chromatic index of any graph with 2s + 2 vertices and maximum degree 2s.
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.
## Abstract This paper proves that if __G__ is a graph (parallel edges allowed) of maximum degree 3, then ฯโฒ~__c__~(__G__)โโคโ11/3 provided that __G__ does not contain __H__~1~ or __H__~2~ as a subgraph, where __H__~1~ and __H__~2~ are obtained by subdividing one edge of __K__ (the graph with three
## Abstract In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117โ134; Russian Math Surveys 23 (1968), 125โ142] conjectured that for any edge chromatic critical graph ${{G}} = ({{V}}, {{E}})$ with maximum degree $\Delta$, $|{{E}}| \geq {{{1}}\over {{2}}}\{(\Delta {{- 1}})|{{V}}| + {{3}}\}$. This conject
## 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