The Chromatic Number of Graph Powers

Authors:
Noga Alon;Bojan Mohar
Affiliations:
Department of Mathematics, Tel Aviv University, Tel Aviv, Israel (e-mail: noga@math.tau.ac.il);Department of Mathematics, University of Ljubljana, 1111 Ljubljana, Slovenia (e-mail: bohan.mohar@uni-lj.si)
Venue:
Combinatorics, Probability and Computing
Year:
2002

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Abstract

It is shown that the maximum possible chromatic number of the square of a graph with maximum degree d and girth g is (1 +o(1))d2 if g = 3, 4, 5 or 6, and is Θ(d2 / log d) if g ≥ 7. Extensions to higher powers are considered as well.