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Signed Circuit Covers of Signed Graphs

Wednesday, October 17th, 2018, 2:00 PM  闵行数学楼102报告厅
摘要: A signed graph G is a graph associated with a mapping σ: E(G) →{+1, -1}. Signed graphs can be used to present surface duals of digraphs embedded in non-orientable surfaces. A signed graph is coverable if each edge is contained in some signed circuit. The edges of a signed circuit in a signed graph corresponds a minimal dependent set in the signed graphic matroid. An oriented signed graph (bidirected graph) has a nowhere-zero integer flow if and only if it is coverable. A signed circuit cover of G is a collection of signed circuits which covers all the edges of G. Signed circuit covers is a new topic drawing attention in recent years. In this talk, we give a brief survey of known results and open problems on signed circuit covers of signed graphs.

报告人简介:范更华教授1988年在加拿大滑铁卢大学获博士学位; 1990年至1997年在美国亚利桑那州立大学数学系任教(1995年获终身教职,Tenured)。1997年中国科学院“百人计划”回国工作,任中国科学院系统科学研究所研究员,离散数学研究中心主任。2001年至2006年任中国数学会组合数学与图论专业委员会主任, 全国组合数学与图论学会理事长,曾任福州大学副校长。范更华教授主要从事图论领域的基础理论研究。他的一个成果以“范定理”、“范条件”被国内外同行广泛引用。一些成果还作为定理出现在国外出版的教科书中。范更华获1998年度国家杰出青年科学基金;获2005年度国家自然科学二等奖。担任国际图论界权威刊物《图论杂志》(Journal of Graph Theory)的执行编委。
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