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arxiv: 1308.4287 · v1 · submitted 2013-08-20 · 🧮 math.CO · math.PR

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On the chromatic number of random regular graphs

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classification 🧮 math.CO math.PR
keywords k-colnumberrandomcertainchromaticconstantd-regularexceeding
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Let G(n,d) be the random d-regular graph on n vertices. For any integer k exceeding a certain constant k_0 we identify a number d_{k-col} such that G(n,d) is k-colorable w.h.p. if d<d_{k-col} and non-k-colorable w.h.p. if d>d_{k-col}.

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