Keynote Speaker:Hongjian Lai

Abstract:

The well-knownChvátal-ErdősTheorem on hamiltonian graphs states that if the stability numbera(G) and the connectivityk(G) satisfy the conditionk(G)>a(G)+s where s{-1,0,1}, then G has a Hamilton path ifs=-1, a Hamilton cycle ifs=0and G is Hamilton-connected ifs=1. There have been many efforts to generalize theChvátal-ErdősConditions and similar conditions in graph theory. We will present some of these extensions. In particular, we will share the ideas of our effort to extend theChvátal-ErdősTheorems within the family of all line graphs.

Speaker Introduction:

Hongjian Lai is a tenured professor and doctoral supervisor at West Virginia University, and mainly studies Eulerian subgraph problems, Hamiltonian cycles and Hamiltonian problems in graph theory and matroid theory, integer flow problems, equidense matroids and equidense network problems, coloring problems and connectivity problems in graph theory. He has published more than 250 academic papers in core journals such as Journal of Combinatorial Theory (Series B), Applied Mathematics and Computation, Journal of Graph Theory, and Discrete Applied Mathematics. He currently serves as the editor ofApplied MathematicsandGraphs and Combinatorics.

Inviter:

Jin Yan Professor of School of Mathematics

Time:

9:00-10:00 on January 7 (Thursday)

Location:

Tencent Meeting:730 753 656

Hosted by: School of Mathematics, Shandong University