Seminars in September 2019

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

    IBS/KAIST Joint Discrete Math Seminar

    A survey of Turán-type subgraph counting problems
    Cory Palmer
    University of Montana, Missoula, MT
    2019/09/19 Tue 4:30PM-5:30PM
    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.
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  • Kevin Hendrey, The minimum connectivity forcing forest minors in large graphs

    IBS/KAIST Joint Discrete Math Seminar

    The minimum connectivity forcing forest minors in large graphs
    Kevin Hendrey
    IBS Discrete Mathematics Group, Daejeon
    2019/09/10 Tue 4:30PM-5:30PM
    Given a graph $G$, we define $\textrm{ex}_c(G)$ to be the minimum value of $t$ for which there exists a constant $N(t,G)$ such that every $t$-connected graph with at least $N(t,G)$ vertices contains $G$ as a minor. The value of $\textrm{ex}_c(G)$ is known to be tied to the vertex cover number $\tau(G)$, and in fact $\tau(G)\leq \textrm{ex}_c(G)\leq \frac{31}{2}(\tau(G)+1)$. We give the precise value of $\textrm{ex}_c(G)$ when $G$ is a forest. In particular we find that $\textrm{ex}_c(G)\leq \tau(G)+2$ in this setting, which is tight for infinitely many forests.
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