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# Kevin Hendrey, The minimum connectivity forcing forest minors in large graphs

## Tuesday, September 10, 2019 @ 4:30 PM - 5:30 PM KST

Room B232,
IBS (기초과학연구원)

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.