The t-Improper Chromatic Number of Random Graphs
نویسندگان
چکیده
منابع مشابه
The t-Improper Chromatic Number of Random Graphs
We consider the t-improper chromatic number of the Erdős-Rényi random graph Gn,p. The t-improper chromatic number χ(G) of G is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. If t = 0, then this is the usual notion of proper colouring. When the edge probability p is constant, we provide a detailed de...
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A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from ( [k] 2 ) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ2(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for p ≥ Cn−1/4 ln n, τ2(Gn,p) = (2 +...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2009
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548309990216