Abstract
Determining the maximum number of edges in an n‐vertex C4‐free graph is a well‐studied problem that dates back to a paper of Erdős from 1938. One of the most important families of C4‐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.