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On an upper bound of a graph's chromatic number, depending on the graph's degree and density

✍ Scribed by O.V Borodin; A.V Kostochka

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
159 KB
Volume
23
Category
Article
ISSN
0095-8956

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## Abstract The upper bound for the harmonious chromatic number of a graph that has been given by Sin‐Min Lee and John Mitchem is improved.

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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.

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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