English

On the independence number of graphs related to a polarity

Combinatorics 2017-04-04 v1

Abstract

We investigate the independence number of two graphs constructed from a polarity of PG(2,q)\mathrm{PG}(2,q). For the first graph under consideration, the Erd\H{o}s-R\'enyi graph ERqER_q, we provide an improvement on the known lower bounds on its independence number. In the second part of the paper we consider the Erd\H{o}s-R\'enyi hypergraph of triangles Hq\mathcal{H}_q. We determine the exact magnitude of the independence number of Hq\mathcal{H}_q, qq even. This solves a problem posed by Mubayi and Williford.

Keywords

Cite

@article{arxiv.1704.00487,
  title  = {On the independence number of graphs related to a polarity},
  author = {Sam Mattheus and Francesco Pavese and Leo Storme},
  journal= {arXiv preprint arXiv:1704.00487},
  year   = {2017}
}