Cookies?
Library Header Image
LSE Research Online LSE Library Services

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. ISSN 0895-4801 (In Press)

[img] Text (Partitioning edge-coloured hypergraphs into few monochromatic tight cycles) - Accepted Version
Download (935kB)

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: 30 May 2020 23:12
URI: http://eprints.lse.ac.uk/id/eprint/104001

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics