Cycles through all finite vertex sets in infinite graphs

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讲座内容：

A closed curve in the Freudenthal compactification |G| of an infinite locally finite graph G is called a Hamiltonian curve if it meets every vertex of G exactly once (and hence it meets every end at least once). We prove that |G| has a Hamiltonian curve if and only if every finite vertex set of G is contained in a cycle of G. We apply this to extend a number of results and conjectures on finite graphs to Hamiltonian curves in infinite locally finite graphs. For example, Barnette’s conjecture (that every finite planar cubic 3-connected bipartite graph is Hamiltonian) is equivalent to the statement that every one-ended planar cubic 3-connected bipartite graph has a Hamiltonian curve. It is also equivalent to the statement that every planar cubic 3-connected bipartite graph with a nowhere-zero 3-flow (with no restriction on the number of ends) has a Hamiltonian curve. However, there are 7-ended planar cubic 3-connected bipartite graphs that do not have a Hamiltonian curve.

主讲人介绍：

李斌龙，西北工业大学副教授，硕士生导师，荷兰Twente大学博士，捷克West Bohemia大学博士后。主要从事图论研究工作，在图的Hamilton性及图的Ramsey理论方面取得一系列研究成果。主持国家自然科学基金青年项目和陕西省基金各一项。在图论方向国际著名期刊J. Graph Theory, European J. Combinatorics等发表论文30余篇。

发布时间：2017-09-28 15:57:43