A note on colour-bias perfect matchings in hypergraphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909088062898176 |
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| author | Balogh, József Treglown, Andrew Zárate-Guerén, Camila |
| author_facet | Balogh, József Treglown, Andrew Zárate-Guerén, Camila |
| contents | A result of Balogh, Csaba, Jing and Pluhár yields the minimum degree threshold that ensures a $2$-coloured graph contains a perfect matching of significant colour-bias (i.e., a perfect matching that contains significantly more than half of its edges in one colour). In this note we prove an analogous result for perfect matchings in $k$-uniform hypergraphs. More precisely, for each $2\leq \ell <k$ and $r\geq 2$ we determine the minimum $\ell$-degree threshold for forcing a perfect matching of significant colour-bias in an $r$-coloured $k$-uniform hypergraph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on colour-bias perfect matchings in hypergraphs Balogh, József Treglown, Andrew Zárate-Guerén, Camila Combinatorics A result of Balogh, Csaba, Jing and Pluhár yields the minimum degree threshold that ensures a $2$-coloured graph contains a perfect matching of significant colour-bias (i.e., a perfect matching that contains significantly more than half of its edges in one colour). In this note we prove an analogous result for perfect matchings in $k$-uniform hypergraphs. More precisely, for each $2\leq \ell <k$ and $r\geq 2$ we determine the minimum $\ell$-degree threshold for forcing a perfect matching of significant colour-bias in an $r$-coloured $k$-uniform hypergraph. |
| title | A note on colour-bias perfect matchings in hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.17073 |