2-Tone Colorings in Graph Products

Jennifer Loe, et al. "2-Tone Colorings in Graph Products." Discussiones Mathematicae Graph Theory 35.1 (2015): 55-72. <http://eudml.org/doc/271235>.

@article{JenniferLoe2015,
abstract = {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.},
author = {Jennifer Loe, Danielle Middelbrooks, Ashley Morris, Kirsti Wash},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {t-tone coloring; Cartesian product; direct product; strong product; -tone coloring; cartesian product},
language = {eng},
number = {1},
pages = {55-72},
title = {2-Tone Colorings in Graph Products},
url = {http://eudml.org/doc/271235},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Jennifer Loe
AU - Danielle Middelbrooks
AU - Ashley Morris
AU - Kirsti Wash
TI - 2-Tone Colorings in Graph Products
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 55
EP - 72
AB - 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.
LA - eng
KW - t-tone coloring; Cartesian product; direct product; strong product; -tone coloring; cartesian product
UR - http://eudml.org/doc/271235
ER -