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arXiv · 1403.4489

Orthogonal polarity graphs and Sidon sets

Michael Tait·Craig Timmons
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Abstract

Determining the maximum number of edges in an $n$-vertex $C_4$-free graph is a well-studied problem that dates back to a paper of Erdős from 1938. One of the most important families of $C_4$-free graphs are the Erdős-Rényi orthogonal polarity graphs. We show that the Cayley sum graph constructed using a Bose-Chowla Sidon set is isomorphic to a large induced subgraph of the Erdős-Rényi orthogonal polarity graph. Using this isomorphism we prove that the Petersen graph is a subgraph of every sufficiently large Erdős-Rényi orthogonal polarity graph.

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Michael Tait, Craig Timmons. 2014-08-10. Orthogonal polarity graphs and Sidon sets. https://arxiv.org/abs/1403.4489

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