Subdivision into i-packings and S-packing chromatic number of some lattices


An i-packing in a graph G is a set of vertices at pairwise distance greater than i. For a nondecreasing sequence of integers S = (s1, s2, . . .), the S-packing chromatic number of a graph G is the least integer k such that there exists a coloring of G into k colors where each set of vertices colored i, i = 1, . . . , k, is an si-packing. This paper describes various subdivisions of an i-packing into j-packings (j > i) for the hexagonal, square and triangular lattices. These results allow us to bound the Spacking chromatic number for these graphs, with more precise bounds and exact values for sequences S = (si, i ∈ N ∗), si = d+ ⌊(i− 1)/n⌋.

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@article{Gastineau2015SubdivisionII, title={Subdivision into i-packings and S-packing chromatic number of some lattices}, author={Nicolas Gastineau and Hamamache Kheddouci and Olivier Togni}, journal={CoRR}, year={2015}, volume={abs/1505.07781} }