2-distance colorings of integer distance graphs

2-Distance Colorings of Integer Distance Graphs

A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1, . . . , k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ2(G) of G is then the mallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d1, . . . , dk}, the integer distance graph G = G(D) is the infinite g...

Edge colorings and total colorings of integer distance graphs

Coloring of integer distance graphs

An integer distance graph is a graph G(D) with the set of integers as vertex set and with an edge joining two vertices u and v if and only if ju ? vj 2 D where D is a subset of the positive integers. We determine the chromatic number (D) of G(D) for some nite distance sets D such as sets of consecutive integers and special sets of cardinality 4.

On Packing Colorings of Distance Graphs

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DISTANCE k COLORINGS OF HAMMING GRAPHS

A coloring of the vertices of a graph G is a distance k coloring of G if and only if any two vertices lying on a path of length less than or equal to k are given different colors. Hamming graphs are Cartesian (or box) products of complete graphs. In this paper, we will consider the interaction between coding theory and distance k colorings of Hamming graphs.