Abstract
AbstractErdős, 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference25 articles.
1. Partitioning 3-colored complete graphs into three monochromatic cycles;Gyárfás;Electron. J. Combin.,2011
2. [7] Conlon, D. (2014) Combinatorial theorems relative to a random set. arXiv:1404.3324
3. [6] Bucić, M. , Korándi, D. and Sudakov, B. (2019) Covering random graphs by monochromatic trees and Helly-type results for hypergraphs. arXiv:1902.05055
4. [17] Korándi, D. , Lang, R. , Letzter, S. and Pokrovskiy, A. (2020) Minimum degree conditions for monochromatic cycle partitioning, to appear in J. Combin. Theory Ser. B.
5. [2] Bal, D. and DeBiasio, L. Personal communication.
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