Matching of Given Sizes in Hypergraphs
| Autor: | Yulin Chang, Huifen Ge, Jie Han, Guanghui Wang |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | SIAM Journal on Discrete Mathematics. 36:2323-2338 |
| ISSN: | 1095-7146 0895-4801 |
| Popis: | For all integers $k,d$ such that $k \geq 3$ and $k/2\leq d \leq k-1$, let $n$ be a sufficiently large integer {\rm(}which may not be divisible by $k${\rm)} and let $s\le \lfloor n/k\rfloor-1$. We show that if $H$ is a $k$-uniform hypergraph on $n$ vertices with $\delta_{d}(H)>\binom{n-d}{k-d}-\binom{n-d-s+1}{k-d}$, then $H$ contains a matching of size $s$. This improves a recent result of Lu, Yu, and Yuan and also answers a question of K\"uhn, Osthus, and Townsend. In many cases, our result can be strengthened to $s\leq \lfloor n/k\rfloor$, which then covers the entire possible range of $s$. On the other hand, there are examples showing that the result does not hold for certain $n, k, d$ and $s= \lfloor n/k\rfloor$. Comment: arXiv admin note: text overlap with arXiv:1507.02362 |
| Databáze: | OpenAIRE |
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