On the independence number of graphs related to a polarity

Sam Mattheus, Francesco Pavese, Leo Storme

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We investigate the independence number of two graphs constructed from a polarity of PG(2, q). For the first graph under consideration, the Erdős-Rényi graph E, we provide an improvement on the known lower bounds on its independence number. In the second part of the paper, we consider the Erdős-Rényi hypergraph of triangles H q. We determine the exact magnitude of the independence number of H q, q even. This solves a problem posed by Mubayi and Williford [On the independence number of the ErdŐs-RÉnyi and projective norm graphs and a related hypergraph, J. Graph Theory, 56 (2007), pp. 113-127, Open Problem 3].

Original languageEnglish
Pages (from-to)96-110
Number of pages15
JournalJournal of Graph Theory
Issue number2
Publication statusPublished - 12 Dec 2018


  • Erdős-Rényi graph
  • independence number
  • polarity graph


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