超图着色缺陷

Pub Date : 2023-10-27 DOI:10.1002/rsa.21190

António Girão, Freddie Illingworth, Alex Scott, David R. Wood

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引用次数: 0

摘要

摘要证明了每一个具有最大度的均匀超图的顶点都可以上色，使得每个顶点最多处于单色边。这个结果，是最好的可能到常数的值，推广了经典的结果Erdős和Lovász谁证明了这种情况。

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Defective coloring of hypergraphs

Abstract We prove that the vertices of every ‐uniform hypergraph with maximum degree may be colored with colors such that each vertex is in at most monochromatic edges. This result, which is best possible up to the value of the constant , generalizes the classical result of Erdős and Lovász who proved the case.

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