# Highly connected subgraphs in sparse graphs

• Henry Liu (Central South University, China)
• Thursday 09 February 2017, 14:30-15:30
• MR12.

Let G be a graph on n vertices with independence number $\alpha$. How large a k-connected subgraph must G contain? It turns out that if n is sufficiently large ($n>\alpha^2 k$ will do), then G always contains a k-connected subgraph on at least $n/\alpha$ vertices. This is sharp, since G might be the disjoint union of $\alpha$ equally-sized cliques. What if n is not sufficiently large? We shall present the (surprisingly complicated) answer when $\alpha=2$ and $\alpha=3$. Some open questions will also be presented.

Joint work with Shinya Fujita (Yokohama City University, Japan) and Amites Sarkar (Western Washington University, USA ).

This talk is part of the Combinatorics Seminar series.