The chromatic number of a graph of girth 5 on a fixed surface

Authors:
Carsten Thomassen
Affiliations:
Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

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Abstract

We prove a color extension result implying that, for every fixed surface S, there are only finitely many 4-color-critical graphs of girth 5 on S. The result is best possible in the sense that there are infinitely many 4-color-critical graphs of girth 4 on S. except when S is the sphere. As a consequence, the chromatic number of graphs of girth 5 on S can be found in polynomial time.