Coloring Powers and Girth
Abstract
Alon and Mohar (2002) posed the following problem: among all graphs $G$ of maximum degree at most $d$ and girth at least $g$, what is the largest possible value of $\chi(G^t)$, the chromatic number of the $t$th power of $G$? For $t\ge 3$, we provide several upper and lower bounds concerning this problem, all of which are sharp up to a constant factor as $d\to \infty$. The upper bounds rely in part on the probabilistic method, while the lower bounds are various direct constructions whose building blocks are incidence structures.
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Information & Authors
Information
Published In
SIAM Journal on Discrete Mathematics
Pages: 1938 - 1949
DOI: 10.1137/15M1035422
ISSN (online): 1095-7146
Copyright
© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 17 August 2015
Accepted: 10 August 2016
Published online: 11 October 2016
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