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 d even.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1269,
author = {Peter Jacko and Stanislav Jendrol'},
title = {Distance coloring of the hexagonal lattice},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {151-166},
zbl = {1074.05035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1269}
}
Peter Jacko; Stanislav Jendrol'. Distance coloring of the hexagonal lattice. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 151-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1269/
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