We show that the intersection graph of a collection of subsets of the plane, where each subset forms an "L" shape whose vertical stem is infinite, has its chromatic number 1 bounded by a function of the order of its largest clique w, where it is shown that ;1<2"4'3"4"'~'-". This proves a special cas
Bounds on the Generalised Acyclic Chromatic Numbers of Bounded Degree Graphs
โ Scribed by Catherine Greenhill; Oleg Pikhurko
- Publisher
- Springer Japan
- Year
- 2005
- Tongue
- English
- Weight
- 143 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
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
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 In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph