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arXiv · 2602.10849

Invariant covers of multipartite hypergraphs

Anton A. Klyachko·Mikhail S. Terekhov
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Abstract

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).

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Anton A. Klyachko, Mikhail S. Terekhov. 2026-02-25. Invariant covers of multipartite hypergraphs. https://arxiv.org/abs/2602.10849

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