## Suil O, Finding a spanning Halin subgraph in 3-connected {K_{1,3},P_5}-free graphs

Finding a spanning Halin subgraph in 3-connected $$\{K_{1,3},P_5\}$$-free graphs
Suil O
Georgia State University, USA
2014/08/28 *Thursday* 4PM-5PM
Room 1409
A Halin graph is constructed from a plane embedding of a tree whose non-leaf vertices have degree at least 3 by adding a cycle through its leaves in the natural order determined by the embedding. In this talk, we prove that every 3-connected $$\{K_{1,3},P_5\}$$-free graph has a spanning Halin subgraph. This result is best possible in the sense that the statement fails if $$K_{1,3}$$ is replaced by $$K_{1,4}$$ or $$P_5$$ is replaced by $$P_6$$. This is a joint work with Guantao Chen, Jie Han, Songling Shan, and Shoichi Tsuchiya.

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