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.
متن کامل2-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...
متن کاملDistance Graphs and T-Coloring
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 ...
متن کامل2-distance Coloring of Sparse Graphs
A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most 2 receive distinct colors. We prove that every graph with maximum degree Δ at least 4 and maximum average degree less that 73 admits a 2-distance (Δ + 1)-coloring. This result is tight. This improves previous known results of Dolama and Sopena.
متن کاملCircular Coloring for Graphs with Distance Constraints
Let G = (V,E) be a simple un-weighted graph, and let → d= (d1, d2, · · ·, dm) be a sequence of positive reals. For a positive real r, let Sr denote the circle on R 2 centered at the origin with circumference r. A circular r−coloring for G with distance constraint → d is a mapping f : V (G) → Sr such that |f(u) − f(v)|r ≥ di, whenever the distance between u and v in G is i (where |x− y|r is the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00099-5