An ?$i$?-packing in a graph ?$G$? is a set of vertices at pairwise distance greater than ?$i$?. For a nondecreasing sequence of integers ?$S=(s_1,s_2,\ldots)$?, 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 ?$i$?, ?$i=1,\ldots,k$?, is an ?$s_i$?-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 ?$S$?-packing chromatic number for these graphs, with more precise bounds and exact values for sequences ?$S=(s_i,i \in \mathbb{N}^*)$?, ?$s_i = d+ \lfloor (i-1)/n \rfloor$?.

Rights

URN

URN:NBN:SI:doc-Z0CK4Z6G

COBISSID

17609561

Added

29.05.2020

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Citation

APA:

Gastineau, Nicolas, Kheddouci, Hamamache, Togni, Olivier (2015). Subdivision into i-packings and S-packing chromatic number of some lattices. Ars mathematica contemporanea, volume 9, issue 2, str. 321-344. URN:NBN:SI:doc-Z0CK4Z6G from http://www.dlib.si

MLA:

Gastineau, Nicolas, Kheddouci, Hamamache, Togni, Olivier. "Subdivision into i-packings and S-packing chromatic number of some lattices." Ars mathematica contemporanea volume 9. issue 2 (2015) str. 321-344.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-Z0CK4Z6G>

Ars mathematica contemporanea
2008-
(Assembly record)