Minimal asymmetric hypergraphs

Yiting Jiang; Jaroslav Nesetril

Minimal asymmetric hypergraphs

Combinatorics 2023-09-20 v4

Authors: Yiting Jiang , Jaroslav Nesetril

Abstract

In this paper, we prove that for any $k\ge 3$ , there exist infinitely many minimal asymmetric $k$ -uniform hypergraphs. This is in a striking contrast to $k=2$ , where it has been proved recently that there are exactly $18$ minimal asymmetric graphs. We also determine, for every $k\ge 1$ , the minimum size of an asymmetric $k$ -uniform hypergraph.

Keywords

hypergraph theory graph theory combinatorial bounds and extremal problems

Cite

@article{arxiv.2111.08077,
  title  = {Minimal asymmetric hypergraphs},
  author = {Yiting Jiang and Jaroslav Nesetril},
  journal= {arXiv preprint arXiv:2111.08077},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2105.10031

Minimal asymmetric hypergraphs

Abstract

Keywords

Cite

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