English

Invariant covers of multipartite hypergraphs

Combinatorics 2026-02-26 v2 Group Theory

Abstract

We prove the following ``symmetric analogue'' of Lov\'asz's estimate (1975): if an rr-partite hypergraph of rank r2r\geqslant2 has a cover of cardinality n<n<\infty, then it admits a cover of cardinality at most nr/2nr/2, which is invariant with respect to all automorphisms preserving the parts. We obtain also symmetric analogues of generalisations of Lov\'asz's estimate due to Aharoni, Holzman, and Krivelevich (1996).

Cite

@article{arxiv.2602.10849,
  title  = {Invariant covers of multipartite hypergraphs},
  author = {Anton A. Klyachko and Mikhail S. Terekhov},
  journal= {arXiv preprint arXiv:2602.10849},
  year   = {2026}
}

Comments

5 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: minor changes

R2 v1 2026-07-01T10:31:53.059Z