报告题目：Hamiltonian properties , branch number and k-trees related graphs
报告人：  Bing Wei
         Department of Mathematics, The University of Mississippi
报告时间：7月10日（周五） 16:00-17:00
报告地点：1218
摘要：Investigating Hamiltonian properties of graphs is a very hot topic in graph theory and k-trees (a generalization of trees for an integer k ≥ 2) are important graphs with some special structures. A long standing conjecture of Chva´tal(1973) states that there exists a finite constant t0 such that every graph G with τ(G) ≥ t0 is Hamiltonian, where τ(G) = min{ |S| ω(G−S) | for any cut-set S ⊂ V (G)} denotes the toughness of a graph G and ω(G − S) is the number of components of G − S. Chen et al.(1998) showed that every 18-tough chordal graph, which is a graph with no induced cycle of length greater than 3, is Hamiltonian. Notice that k-trees are special chordal graphs, we introduce a new parameter, the branch number of G, which is easier to calculate and work with than the toughness for k-trees. Some results on the relationships between the branch number and other graph parameters will be presented. Applying the branch number, we will explore some Hamiltonian properties for k-trees and its related graphs. Further research problems will also be proposed.

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