SEMINARS
Extremal $H$-free Planar Graphs

2018-07-02　16:00 — 17:30

1202, Math Building

Zi-Xia Son

University of Central Florida, USA

We   study the topic of extremal" planar graphs initiated by Chris Dowden in 2016, that is,   how many edges
can a planar graph on $n$ vertices have without containing a given smaller graph?   Let  $ex_{_\mathcal{P}}(n,H)$ denote  the maximum number of edges in a planar graph on $n$ vertices without containing   a given graph $H$ as a subgraph. Unlike classic Tur\'an number of graphs, one can easily see that  $ex_{_\mathcal{P}}(n,H)=3n-6$ when   $\Delta(H)\ge7$ or  $H$ contains $K_4$ as a proper subgraph.  However, determining the exact values of $ex_{_\mathcal{P}}(n,H)$ when $H$ is sparse is far from trivial.  In this talk, we survey recent progress on this topic.  \\

This is joint work with Yongxin Lan and Yongtang Shi.