A linear programming bound obtained by restricting the Lovász theta number to local graphs of Paley graphs rivals the Hanson-Petridis closed-form bound and is conjectured to improve on it for infinitely many cases.
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Linear programming bounds for cliques in Paley graphs
A linear programming bound obtained by restricting the Lovász theta number to local graphs of Paley graphs rivals the Hanson-Petridis closed-form bound and is conjectured to improve on it for infinitely many cases.