Distance Graphs with Finite Chromatic Number
نویسندگان
چکیده
منابع مشابه
Distance graphs with maximum chromatic number
Let D be a finite set of integers. The distance graph G(D) has the set of integers as vertices and two vertices at distance d ∈ D are adjacent in G(D). A conjecture of Xuding Zhu states that if the chromatic number of G(D) achieves its maximum value |D| + 1 then the graph has a clique of order |D|. We prove that the chromatic number of a distance graph with D = {a, b, c, d} is five if and only ...
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Let Z be the set of all integers and M a set of positive integers. The distance graph G(Z,M) generated by M is the graph with vertex set Z and in which i and j are adjacent whenever |i − j| ∈ M . Supported in part by the National Science Foundation under grant DMS 9805945. Supported in part by the National Science Council, R. O. C., under grant NSC892115-M-110-012.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2093