Coloring of distance graphs with intervals as distance sets
نویسندگان
چکیده
منابع مشابه
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.
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Given positive integers m, k and s with m > ks, let Dm,k,s represent the set {1, 2, · · · ,m} − {k, 2k, · · · , sk}. The distance graph G(Z,Dm,k,s) has as vertex set all integers Z and edges connecting i and j whenever |i − j| ∈ Dm,k,s. The chromatic number and the fractional chromatic number of G(Z,Dm,k,s) are denoted by χ(Z,Dm,k,s) and χf (Z,Dm,k,s), respectively. For s = 1, χ(Z,Dm,k,1) was s...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2005
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.01.017