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Monochromatic cycle partitions in random graphs
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-08-14 , DOI: 10.1017/s0963548320000401 Richard Lang , Allan Lo
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-08-14 , DOI: 10.1017/s0963548320000401 Richard Lang , Allan Lo
Erdős, Gyárfás and Pyber showed that every r -edge-coloured complete graph K n can be covered by 25 r 2 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 1000r 4 log r vertex-disjoint monochromatic cycles. This answers a question of Korándi, Mousset, Nenadov, Škorić and Sudakov.
中文翻译:
随机图中的单色循环分区
Erdős、Gyárfás 和 Pyber 表明,每个r - 边色完整图ķ n 可以覆盖25r 2 日志r 顶点不相交的单色循环(独立于n )。在这里,我们将他们的结果扩展到二项式随机图的设置。也就是说,我们证明如果$p = p(n) = \Omega(n^{-1/(2r)})$ ,那么很有可能任何r -边缘彩色G (n ,p ) 最多可以覆盖 1000r 4 日志r 顶点不相交的单色循环。这回答了 Korándi、Mousset、Nenadov、Škorić 和 Sudakov 的问题。
更新日期:2020-08-14
中文翻译:
随机图中的单色循环分区
Erdős、Gyárfás 和 Pyber 表明,每个