## Abstract

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 language | English |
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Pages (from-to) | 96-110 |

Number of pages | 15 |

Journal | Journal of Graph Theory |

Volume | 92 |

Issue number | 2 |

DOIs | |

Publication status | Published - 12 Dec 2018 |

## Keywords

- Erdős-Rényi graph
- independence number
- polarity graph