Orthogonal polarity graphs and Sidon sets
Combinatorics
2014-08-12 v3
Abstract
Determining the maximum number of edges in an -vertex -free graph is a well-studied problem that dates back to a paper of Erd\H{o}s from 1938. One of the most important families of -free graphs are the Erd\H{o}s-R\'enyi 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 Erd\H{o}s-R\'enyi orthogonal polarity graph. Using this isomorphism we prove that the Petersen graph is a subgraph of every sufficiently large Erd\H{o}s-R\'enyi orthogonal polarity graph.
Keywords
Cite
@article{arxiv.1403.4489,
title = {Orthogonal polarity graphs and Sidon sets},
author = {Michael Tait and Craig Timmons},
journal= {arXiv preprint arXiv:1403.4489},
year = {2014}
}
Comments
The authors would like to thank Jason Williford for noticing an error in the proof of Theorem 1.2 in the previous version. This error has now been corrected