Title：Spanning trees with few leaves and branch vertices

Abstract：A leaf of a tree is a vertex with degree 1 and a branch vertex of a tree is a vertex with degree at least 3. Clearly, a hamiltonian path can be regarded as a spanning tree with exact two leaves, or a spanning tree with no branch vertex. Therefore, looking for conditions which ensure the existence of a spanning tree with bounded few leaves or (and) few branch vertices can be seen as a generalized problem of hamiltonian path problem. In this report, we give some sufficient conditions for graphs to have a spanning with few leaves or (and) few branch vertices.

Speaker：Cai Junqing, Ph.D., received her Ph.D. from Lanzhou University in 2012 under the Professor Li Hao, the Changjiang Scholar Chair Professor, and is currently working at Tianjin Normal University. Her main research area is the structure of graphs, especially the problems of circles and spanning trees in graphs. At present, she has published more than 30 SCI papers and presided over and completed 4 projects such as the National Natural Science Foundation of China Youth Project. In March 2016, she was a six-month academic visiting scholar at the University of Paris-Saclay France.

Date：2:00pm-5:00pm 2023-10-16（Monday）.

Tencent Meeting ID：848-807-955

Organizer：School of Mathematical Science

Students and teachers who are interested in graph theory are welcome.