随机图中的单色循环划分

Combinatorics, Probability and Computing Pub Date : 2018-07-17 DOI:10.1017/S0963548320000401

R. Lang, A. Lo

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引用次数: 8

摘要

摘要Erdős, Gyárfás和Pyber证明了每个r边彩色完全图Kn可以被25个r2 log r顶点不相交的单色循环(与n无关)覆盖。这里我们将他们的结果推广到二项随机图的设置。也就是说，我们证明了如果$p = p(n) = \Omega(n^{-1/(2r)})$，那么在高概率下任何r边有色的G(n, p)最多可以被1000r4 log r顶点不相交的单色循环覆盖。这回答了Korándi, Mousset, Nenadov， Škorić和Sudakov的问题。

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Monochromatic cycle partitions in random graphs

Abstract Erdős, Gyárfás and Pyber showed that every r-edge-coloured complete graph Kn can be covered by 25 r2 log r vertex-disjoint monochromatic cycles (independent of n). Here we extend their result to the setting of binomial random graphs. That is, we show that if $p = p(n) = \Omega(n^{-1/(2r)})$ , then with high probability any r-edge-coloured G(n, p) can be covered by at most 1000r4 log r vertex-disjoint monochromatic cycles. This answers a question of Korándi, Mousset, Nenadov, Škorić and Sudakov.

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Combinatorics, Probability and Computing

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