English

The Szemer\'edi-Petruska conjecture for a few small values

Combinatorics 2020-10-06 v1

Abstract

Let H be a 3-uniform hypergraph of order n with clique number k such that the intersection of all maximum cliques of H is empty. For fixed m=n-k, Szemer\'edi and Petruska conjectured the sharp bound n(m+22)n\leq {m+2\choose 2}. In this note the conjecture is verified for m=2,3 and 4.

Keywords

Cite

@article{arxiv.2010.01228,
  title  = {The Szemer\'edi-Petruska conjecture for a few small values},
  author = {Adam S. Jobson and André E. Kézdy and Jenő Lehel},
  journal= {arXiv preprint arXiv:2010.01228},
  year   = {2020}
}