广义Mycielski图的色拉姆齐数

Pub Date : 2023-01-01 DOI:10.7151/dmgt.2499

Claude Tardif

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引用次数: 0

摘要

。我们重新审视了色拉姆齐数的Burr-Erd“os-Lov”猜想。我们证明了除了朱旭定基于分数阶色数的证明外，它还允许一个基于Lov´asz φ参数的证明。然而，由于广义Mycielski图的色拉姆齐数太大，没有基于色数拓扑下界的证明。我们证明了除k4以外的4色广义Mycielski图都具有色Ramsey数14，并且n色广义Mycielski图都具有至少2 n/ 4的色Ramsey数。

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Chromatic Ramsey numbers of generalised Mycielski graphs

. We revisit the Burr–Erd˝os–Lov´asz conjecture on chromatic Ramsey numbers. We show that it admits a proof based on the Lov´asz ϑ parame- ter in addition to the proof of Xuding Zhu based on the fractional chromatic number. However, there are no proofs based on topological lower bounds on chromatic numbers, because the chromatic Ramsey numbers of generalised Mycielski graphs are too large. We show that the 4-chromatic generalised Mycielski graphs other than K 4 all have chromatic Ramsey number 14, and that the n -chromatic generalised Mycielski graphs all have chromatic Ramsey number at least 2 n/ 4 .

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