报告时间：6月19日（周二）下午15:00-17:30

报告地点：管理科研楼1308教室

报告一

报告人： Prof. Hong-Jian Lai (West Virginia University, USA)

报告题目: Edge-disjoint spanning trees, edge connectivity and eigenvalues in graphs

摘  要：Seymour proposed a problem on the relationship between eigenvalues of a simple graph $G$ and bounds of $/tau(G)$, the maximum number of edge-disjoint spanning trees of $G$. In this talk, we will present a brief history of the problem and some of the recent progresses made towards this problem.

报告二

报告人： Prof. Cun-Quan Zhang (West Virginia University, USA)

报告题目: 3-ows for 6-edge-connected graphs

摘  要：It was conjectured by Tutte (1970's) that every 4-edge connected graph admits a nowhere-zero 3-flow. Jaeger, Linial, Payan and Tarsi (1992 JCTB) further conjectured that every 5-edge-connected graph is Z3-connected. A weak version of the 3-flow conjecture was proposed by Jaeger (1979) that there is an integer h such that every h-edge-connected graph admits a nowhere-zero 3-flow. Thomassen (JCTB 2012) recently solved this open problem by proving that every 8-edge-connected graph is Z3-connected and admits a nowhere-zero 3-flow. In this paper, Thomassen's result is further improved that every 6-edge-connected graph is Z3-connected and admits a nowhere-zero 3- flow. Note that it was proved by Kochol (2001 JCTB) that it suffices to prove the 3-flow conjecture for 5-edge-connected graphs. (Joint work with L. M. Lovász, C. Thomassen, Yezhou Wu――former student of USTC)

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                 中科院吴文俊数学重点实验室

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