Coloring of some integer distance graphs

摘要

An integer distance graph is a graph G(Z, D) with the integer set Z as vertex set, in which an edge joining two vertices u and v if and only if | u - v | ∈ D, where D is a set of natural numbers. Using a related theorem in combinatorics and some conclusions known to us in the coloring of the distance graph, the chromatic number _X(G) is determined in this paper that is of the distance graph G(Z, D) for some finite distance sets D containing {2, 3} with D = 4 and containing {2, 3, 5} with | D | = 5 by the method in which the combination of a few periodic colorings.