### Colloquium at Math Department at WVU, Spring 2020

** Date: **Wednesday, March 11, 4-4:50pm. Preceded with refreshments, 3:30-4:00pm, in the math faculty lounge.

** Location: ** 315 Armstrong Hall

** Speaker (notice change)**: Dr. Dong Ye, Middle Tennessee State University; invited by Prof. Rong Luo

** Title: ** Connectivity for Small Graph Linkages

** Abstract:**
For a given simple graph $H$, a graph $G$ is {\em $H$-linked} if, for
every injection $\varphi: V(H) \to V(G)$, the graph $G$ contains a subdivision of $H$
with $\varphi(v)$ corresponding to $v$, for each $v\in V(H)$. Let $f(H)$ be the
minimum integer $k$ such that every $k$-connected graph is $H$-linked.
It is known that $|E(G)|\le f(H)\le 10 |E(G)|$. Among simple graphs $H$ with at least
four vertices, the exact value $f(H)$ is only know when $H$ is a star, or a path
with four vertices, or a cycle with four vertices, or a disjoint union of two $K_2$'s.
In this talk, we introduce some recent results on connectivity on small graph linkages.