Invariant covers of multipartite hypergraphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918355086082048 |
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| author | Klyachko, Anton A. Terekhov, Mikhail S. |
| author_facet | Klyachko, Anton A. Terekhov, Mikhail S. |
| contents | We prove the following ``symmetric analogue'' of Lovász's estimate (1975): if an $r$-partite hypergraph of rank $r\geqslant2$ has a cover of cardinality $n<\infty$, then it admits a cover of cardinality at most $nr/2$, which is invariant with respect to all automorphisms preserving the parts. We obtain also symmetric analogues of generalisations of Lovász's estimate due to Aharoni, Holzman, and Krivelevich (1996). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant covers of multipartite hypergraphs Klyachko, Anton A. Terekhov, Mikhail S. Combinatorics Group Theory We prove the following ``symmetric analogue'' of Lovász's estimate (1975): if an $r$-partite hypergraph of rank $r\geqslant2$ has a cover of cardinality $n<\infty$, then it admits a cover of cardinality at most $nr/2$, which is invariant with respect to all automorphisms preserving the parts. We obtain also symmetric analogues of generalisations of Lovász's estimate due to Aharoni, Holzman, and Krivelevich (1996). |
| title | Invariant covers of multipartite hypergraphs |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2602.10849 |