Speaker: Kyle Murphy
Title: Maximizing five cycles in K_r-free graphs
Abstract:
The Erdos Pentagon problem asks for the maximum number of five-cycles in a triangle-free graph.
This was solved asymptotically in 2012 by Grzesik, and independently in 2013, Hatami, Hladky,
Kral, Norin, and Razborov. Later, Lidicky and Pfender extended the result to all values of n.
Using flag algebras, we consider a generalization of the Erdos Pentagon problem to larger complete
graphs, showing that asymptotically, the Turan graph maximizes the number of five-cycles among
all K_r-free graphs for $r \geq 4$. This generalization was suggested by Cory Palmer.
This is joint work with Bernard Lidicky.