勷勤数学•专家报告

题      目：DP color functions of hypergraphs

报  告  人： 万良霞 副教授  (邀请人：周波)

                                       北京交通大学

时      间： 11月6日  10：00-11:00

地     点：数科院东楼401

报告人简介:

        博士毕业于北京交通大学（2006年），2008年完成清华大学数学科学系博士后研究。2009年至今任教于北京交通大学。主要从事拓扑图论、低维拓扑及复杂系统建模研究，涉及图的嵌入分布、网络与组合优化、运筹学等方向。曾访问University of California, Los Angeles数学系。主持包括国家自然科学基金在内的多项基金项目的研究, 任中国运筹学会数学与智能分会理事等。

摘      要：

       The chromatic function P(G,k), in fact a polynomial, of a graph G was introduced by Birkhoff in 1912 with the hope of proving the Four Color Conjecture. This function for a graph is naturally extended to that for a hypergraph. In this talk the DP color function PDP(H,k) of a hypergraph H is introduced for all positive integer k. This is the minimum value PDP(H,F) taken over all k-fold covers of H. It is an extension of its chromatic polynomial P(H,k) with the property that PDP(H,k) ≤P(H,k). We obtain an upper bound for PDP(H,k),when H is a connected r-uniform hypergraph for r≥2 and the upper bound is attained if and only if H is a r-uniform hypertree. We also show that PDP(H,k) =P(H,k) holds when H is a r-uniform hypertree or a unicycle linear r-uniform hypergraph with odd cycle for r≥3. These conclusions coincide with the known results of graphs.

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