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
Text (Partitioning edge-coloured hypergraphs into few monochromatic tight cycles)
- Accepted Version
Download (935kB) |
|
Text (Partitioning edge-coloured hypergraphs into few monochromatic tight cycles)
- Published Version
Download (709kB) |
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: | 14 Sep 2024 08:15 |
URI: | http://eprints.lse.ac.uk/id/eprint/104001 |
Actions (login required)
View Item |