Title:Thomassen hamiltonian line graph conjecture and spanning connectivity of line graphs

Keynote Speaker:Hong-Jian Lai

Abstart:

There have been some fascinating conjectures on the hamiltonicity of line graphs,led by the Thomassen conjecture that every 4-connected line graph is Hamiltonian. From the view point of Menger Theorem, the Hamiltonian problem can be stated as a spanning connectivity problem, and the Thomassen conjecture mentioned above is equivalent to saying that every 4-connected line graph is 2-spanning connected. By Menger Theorem the spanning connectivity of a graph is upper bounded by the connectivity. A graph G is maximally spanning connected if its spanning connectivity equals the connectivity. The recent attempt of finding the necessary and sufficient version of Thomassen conjecture also suggests to characterize maximally spanning connected line graphs. In this talk, we will report some of the recent progresses and a few new conjectures and open problems in this direction.

Brief Introdution to the Keynote Speaker：

Hong-Jian Lai, West Virginia University

Inviter：

Yan Jin  ,professor in School of Mathematics

Time：

8:00,December 9(Monday)

Location：

Lecture Hall924  Block B, Zhixin Building, Central Campus

   Sponsored by: School of Mathematics, Shandong University