English

Triangle-intersecting families on eight vertices

Combinatorics 2011-02-10 v1

Abstract

Simonovits and S\'{o}s conjectured that the maximal size of a triangle-intersecting family of graphs on nn vertices is 2(n2)32^{\binom{n}{2}-3}. Their conjecture has recently been proved using spectral methods. We provide an elementary proof of the special case of 88 vertices using a partition argument.

Keywords

Cite

@article{arxiv.1102.1764,
  title  = {Triangle-intersecting families on eight vertices},
  author = {Yuval Filmus},
  journal= {arXiv preprint arXiv:1102.1764},
  year   = {2011}
}
R2 v1 2026-06-21T17:23:38.816Z