Partitioning edge-colored hypergraphs into few monochromatic tight cycles

Bustamante, Sebastián, Corsten, Jan, Frankl, Nora, Pokrovskiy, Alexey and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2020) Partitioning edge-colored hypergraphs into few monochromatic tight cycles. SIAM Journal on Discrete Mathematics, 34 (2). 1460 – 1471. ISSN 0895-4801

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Abstract

Confirming a conjecture of Gyárfás, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural numbers p and r, the vertices of every r-edge-colored complete graph can be partitioned into a bounded number of pth powers of cycles, settling a problem of Elekes, Soukup, Soukup, and Szentmiklóssy [Discrete Math., 340 (2017), pp. 2053-2069]. In fact we prove a common generalization of both theorems which further extends these results to all host hypergraphs of bounded independence number.

Item Type:	Article
Official URL:	https://epubs.siam.org/journal/sjdmec
Additional Information:	© 2020 Society for Industrial and Applied Mathematics
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	06 Apr 2020 16:48
Last Modified:	15 Nov 2025 12:11
URI:	http://eprints.lse.ac.uk/id/eprint/104001

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