2-Tone Colorings in Graph Products
Jennifer Loe ; Danielle Middelbrooks ; Ashley Morris ; Kirsti Wash
Discussiones Mathematicae Graph Theory, Tome 35 (2015), p. 55-72 / Harvested from The Polish Digital Mathematics Library
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A variation of graph coloring known as a t-tone k-coloring assigns a set of t colors to each vertex of a graph from the set {1, . . . , k}, where the sets of colors assigned to any two vertices distance d apart share fewer than d colors in common. The minimum integer k such that a graph G has a t- tone k-coloring is known as the t-tone chromatic number. We study the 2-tone chromatic number in three different graph products. In particular, given graphs G and H, we bound the 2-tone chromatic number for the direct product G×H, the Cartesian product G□H, and the strong product G⊠H.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:271235 
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Jennifer Loe; Danielle Middelbrooks; Ashley Morris; Kirsti Wash. 2-Tone Colorings in Graph Products. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 55-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1773/

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