A Bound on the Total Chromatic Number
โ Scribed by Michael Molloy; Bruce Reed
- Book ID
- 105746884
- Publisher
- Springer-Verlag
- Year
- 1998
- Tongue
- English
- Weight
- 481 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In 1969, Ore and Plummer defined an angular coloring as a natural extension of the Four Color Problem: a face coloring of a plane graph where faces meeting even at a vertex must have distinct colors. A natural lower bound is the maximum degree 2 of the graph. Some graphs require w 3 2 2x colors in a
We give an upper bound on the chromatic number of a graph in terms of its maximum degree and the size of the largest complete subgraph. Our result extends a theorem due to i3rook.s.
## Abstract A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number ฯ^__c__^. Let ฮ^\*^ be the maximum face degree of a graph. There exist
Let C be a simple graph. let JiGI denote the maximum degree of it\ \erlicek. ,III~ Ic~r \ 1 C; 1 denote irs chromatic pumber. Brooks' Theorem asserb lha1 ytG I'--AI G I. unk\\ C; hd.. .I component that is a COI lplete graph K,,,,\_ ,. or ullesq .I1 G I = 2 and G ha\ ;~n c~rld C\CIC
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.