15,885 research outputs found
Orthogonal polarity graphs and Sidon sets
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.Comment: 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
correcte
A sequence of triangle-free pseudorandom graphs
A construction of Alon yields a sequence of highly pseudorandom triangle-free
graphs with edge density significantly higher than one might expect from
comparison with random graphs. We give an alternative construction for such
graphs.Comment: 6 page
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