Degenerate and star colorings of graphs on surfaces

Authors:
Bojan Mohar;Simon Špacapan
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada;University of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia
Venue:
European Journal of Combinatorics
Year:
2012

Citing 5
Cited 0

Grad and classes with bounded expansion I. Decompositions

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A conjecture of Borodin and a coloring of Grünbaum

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Star coloring of graphs

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The Two-Coloring Number and Degenerate Colorings of Planar Graphs

SIAM Journal on Discrete Mathematics
Acyclic coloring of graphs

Random Structures & Algorithms

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Abstract

We study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. (2004) [8]: If G is a graph of maximum degree @D, then G admits a degenerate star coloring using O(@D^3^/^2) colors. We use this result to prove that every graph of genus g admits a degenerate star coloring with O(g^3^/^5) colors. It is also shown that these results are sharp up to a logarithmic factor.