2019-09-10 Kevin Hendrey, The minimum connectivity forcing forest minors in large graphs
Автор: IBS Discrete Mathematics Group
Загружено: 2019-09-17
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IBS Discrete Mathematics Group
Discrete Math Seminar
Kevin Hendrey, The minimum connectivity forcing forest minors in large graphs
September 10 2019, Tuesday @ 4:30 PM ~ 5:30 PM
Room B232, IBS (기초과학연구원)
Speaker
Kevin Hendrey
IBS Discrete Mathematics Group
https://sites.google.com/view/kevinhe...
Given a graph $G$, we define $ex_c(G)$ 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 $ex_c(G)$ is known to be tied to the vertex cover number $\tau(G)$, and in fact $\tau(G) \leq ex_c(G) \leq (31/2)(\tau(G)+1)$. We give the precise value of $ex_c(G)$ when $G$ is a forest. In particular we find that $ex_c(G) \leq \tau(G)+2$ in this setting, which is tight for infinitely many forests.
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