On September 10, 2019, Kevin Hendrey at IBS Discrete Mathematics Group presented his work on the minimum connectivity to force a minor isomorphic to a fixed forest in a large graph. The title of his talk was “The minimum connectivity forcing forest minors in large graphs”.

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

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.

## Welcome Kevin Hendrey, a new research fellow in the IBS discrete mathematics group

The IBS discrete mathematics group welcomes Dr. **Kevin Hendrey**, a new research fellow at the IBS discrete mathematics group from August 16, 2019.

He received his Ph.D. from the School of Mathematics, Monash University in Australia in 2019 under the supervision of Prof. David R. Wood. Welcome!