Elsevier

Discrete Mathematics

Volume 286, Issues 1–2, 6 September 2004, Pages 147-149
Discrete Mathematics

Cycle lengths and chromatic number of graphs

Dedicated to Paul Erdős
https://doi.org/10.1016/j.disc.2003.11.055Get rights and content
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Abstract

For a simple finite graph G let Co(G) and Ce(G) denote the set of odd cycle lengths and even cycle lengths in a graph G, respectively. We will show that the chromatic number χ(G) of G satisfies: χ(G)⩽ min{2r+2,2s+3}⩽r+s+2, if |Co(G)|=r and |Ce(G)|=s.

MSC

05C15

Keywords

Chromatic number
Cycle length
k-degenerate graph

Cited by (0)

1

Research supported in part by the Slovak VEGA Grant 2/1131/21.