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A bound on the chromatic number of the square of a planar graph

โœ Scribed by Michael Molloy; Mohammad R. Salavatipour


Book ID
108167375
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
346 KB
Volume
94
Category
Article
ISSN
0095-8956

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๐Ÿ“œ SIMILAR VOLUMES


A bound on the chromatic number of a gra
โœ Paul A. Catlin ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 392 KB

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.

Another bound on the chromatic number of
โœ Paul A. Catlin ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 422 KB

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

The star-chromatic number of planar grap
โœ Moser, David ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 127 KB ๐Ÿ‘ 2 views

The star-chromatic number of a graph, a parameter introduced by Vince, is a natural generalization of the chromatic number of a graph. Here we construct planar graphs with star-chromatic number r, where r is any rational number between 2 and 3, partially answering a question of Vince.