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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08406 |
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| _version_ | 1866913730118287360 |
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| author | Frankl, Peter Wang, Jian |
| author_facet | Frankl, Peter Wang, Jian |
| contents | The matching number of a $k$-graph is the maximum number of pairwise disjoint edges in it. The $k$-graph is called $t$-resilient if omitting $t$ vertices never decreases its matching number. The complete $k$-graph on $sk+k-1$ vertices has matching number $s$ and it is easily seen to be $(k-1)$-resilient. We conjecture that this is maximal for $k=3$ and $s$ arbitrary. The main result verifies this conjecture for $s=2$. Then Theorem 1.9 provides a considerable improvement on the known upper bounds for $s\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On resilient hypergraphs Frankl, Peter Wang, Jian Combinatorics The matching number of a $k$-graph is the maximum number of pairwise disjoint edges in it. The $k$-graph is called $t$-resilient if omitting $t$ vertices never decreases its matching number. The complete $k$-graph on $sk+k-1$ vertices has matching number $s$ and it is easily seen to be $(k-1)$-resilient. We conjecture that this is maximal for $k=3$ and $s$ arbitrary. The main result verifies this conjecture for $s=2$. Then Theorem 1.9 provides a considerable improvement on the known upper bounds for $s\geq 3$. |
| title | On resilient hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.08406 |