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Partitioning edge-coloured hypergraphs into few monochromatic tight cycles

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

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Identification Number: 10.1137/19M1269786

Abstract

Confirming a conjecture of Gyárfás, we prove that, for all natural numbers k and r, the vertices of every r-edge-coloured 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-coloured complete graph can be partitioned into a bounded number of p-th powers of cycles, settling a problem of Elekes, Soukup, Soukup and Szentmiklóssy. In fact we prove a common generalisation 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: 03 Sep 2020 23:20
URI: http://eprints.lse.ac.uk/id/eprint/104001

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