Distance coloring of the hexagonal lattice

Jacko, Peter and Jendrol', Stanislav (2005) Distance coloring of the hexagonal lattice. Discussiones Mathematicae Graph Theory, 25 (1-2). pp. 151-166. ISSN 1234-3099

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Abstract

Motivated by the frequency assignment problem we study the d-distant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted χd(H), is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of χd(H) for any d odd and estimations for any d even.