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 -partite hypergraph of rank has a cover of cardinality , then it admits a cover of cardinality at most , 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