Geodesic
On the packing chromatic number of square and hexagonal lattice
Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 13-22.

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The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes X1, …, Xk, with the condition that vertices in Xi have pairwise distance greater than i. We show that the packing chromatic number for the hexagonal lattice ℋ is 7. We also investigate the packing chromatic number for infinite subgraphs of the square lattice ℤ 2 with up to 13 rows. In particular, we establish the packing chromatic number for P6□ ℤ and provide new upper bounds on these numbers for the other subgraphs of interest. Finally, we explore the packing chromatic number for some infinite subgraphs of ℤ 2□ P2. The results are partially obtained by a computer search.
DOI : 10.26493/1855-3974.255.88d
Keywords: Packing chromatic number, hexagonal lattice, square lattice, computer search 
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Danilo Korže; Aleksander Vesel. On the packing chromatic number of square and hexagonal lattice. Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 13-22. doi : 10.26493/1855-3974.255.88d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.255.88d/

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