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2-Tone Colorings in Graph Products

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Loe J., Middelbrooks D., Morris A., Wash K.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 1

55-72

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.

Worm Colorings

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Goddard W., Wash K., Xu H.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 3

571-584

Given a coloring of the vertices, we say subgraph H is monochromatic if every vertex of H is assigned the same color, and rainbow if no pair of vertices of H are assigned the same color. Given a graph G and a graph F, we define an F-WORM coloring of G as a coloring of the vertices of G without a rainbow or monochromatic subgraph H isomorphic to F. We present some results on this concept especially as regards to the existence, complexity, and optimization within certain graph classes. The focus is on the case that F is the path on three vertices.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Wash K.

1 Goddard W.

1 Loe J.

1 Middelbrooks D.

1 Morris A.

1 Xu H.

2 2015

Wyniki wyszukiwania

2-Tone Colorings in Graph Products

Worm Colorings