Distance Graphs and T-Coloring
نویسندگان
چکیده
We discuss relationships among T-colorings of graphs and chromatic numbers, fractional chromatic numbers, and circular chromatic numbers of distance graphs. We first prove that for any finite integral set T that contains 0, the asymptotic T-coloring ratio R(T ) is equal to the fractional chromatic number of the distance graph G(Z, D), where D=T&[0]. This fact is then used to study the distance graphs with distance sets of the form Dm, k=[1, 2, ..., m]&[k]. The chromatic numbers and the fractional chromatic numbers of G(Z, Dm, k) are determined for all values of m and k. Furthermore, circular chromatic numbers of G(Z, Dm, k) for some special values of m and k are obtained. 1999 Academic Press
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 75 شماره
صفحات -
تاریخ انتشار 1999