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Cory Palmer, A survey of Turán-type subgraph counting problems

September 19 Thursday @ 4:30 PM - 5:30 PM

Room B232, IBS (기초과학연구원)


Cory T. Palmer
University of Montana, Missoula, MT

Let $F$ and $H$ be graphs. The subgraph counting function $\operatorname{ex}(n,H,F)$ is defined as the maximum possible number of subgraphs $H$ in an $n$-vertex $F$-free graph. This function is a direct generalization of the Turán function as $\operatorname{ex}(n,F)=\operatorname{ex}(n,K_2,F)$. The systematic study of $\operatorname{ex}(n,H,F)$ was initiated by Alon and Shikhelman in 2016 who generalized several classical results in extremal graph theory to the subgraph counting setting. Prior to their paper, a number of individual cases were investigated; a well-known example is the question to determine the maximum number of pentagons in a triangle-free graph. In this talk we will survey results on the function $\operatorname{ex}(n,H,F)$ including a number of recent papers. We will also discuss this function’s connection to hypergraph Turán problems.


September 19 Thursday
4:30 PM - 5:30 PM
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Room B232
IBS (기초과학연구원)


Sang-il Oum