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Distance coloring of the hexagonal lattice

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<mark>Journal publication date</mark>2005
<mark>Journal</mark>Discussiones Mathematicae Graph Theory
Issue number1-2
Volume25
Number of pages16
Pages (from-to)151-166
Publication StatusPublished
<mark>Original language</mark>English

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.