Distance coloring of the hexagonal lattice
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 , is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of for any d odd and estimations for any...