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

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 -free graph has a spanning Halin subgraph. This result is best possible in the sense that the statement fails if is replaced by or is replaced by . This is a joint work with Guantao Chen, Jie Han, Songling Shan, and Shoichi Tsuchiya.