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图与组合系列讲座之八(罗荣)

  发布日期:2017-05-26  浏览量:417


报告题目:  Flows of signed graphs

: 罗荣(美国西弗吉尼亚大学, 教授)

报告时间:  201764(周日)下午4:30-5:30

报告地点: 磬苑校区澳门赌搏网站大全H306

报告摘要Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modulo flows and integer-valued flows for ordinary graphs. However, such equivalence does not hold any more for signed graphs. This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. We generalize some early results by Xu and Zhang (Discrete Math. 299, 2005), Schubert and Steffen (European J. Combin. 48, 2015), and Zhu (J. Combin. Theory Ser. B 112, 2015), and show that, for signed graphs, every modulo -flow with  can be converted/ extended into an integer-valued flow.

In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph has a nowhere-zero 6-flow. The best published result is Zyka's 30-flow and was recently improved to 12-flow by DeVos. As an application of our aforementioned results, we further strengthen DeVos' result for bridgeless signed graphs, and show that every bridgeless flow-admissible signed graph admits a nowhere-zero 11-flow. We also verify Bouchet's conjecture for signed graphs without edge-disjoint unbalanced circuits. This is joint work with Jian Cheng, You Lu, and Cun-Quan Zhang.

 

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专家概况: 罗荣,美国西弗吉尼亚大学(West Virginia UniversityUSA)数学系教授、博士生导师,美国数学学会委员,曾任中西部图论会议、AMS东南会议图论会议、坎伯兰会议大会组委会委员,现任Journal of Proteomics & BioinformaticsOpen Journal of Discrete MathematicsISRN Discrete Mathematics等期刊编委。 主要从事图论、组合、组合矩阵论、图论在化学和生物学中的应用等方面的研究。2007-2008年在中田纳西州立大学荣获卓越出版奖;2006-2007年在中田纳西州立大学荣获杰出科研奖励;2003-2004年在中田纳西州立大学荣获杰出研究员奖。

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