Proper orientations and proper orientation number
【2022.12.12 3:00pm, 腾讯会议】

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Proper orientations and proper orientation number
【2022.12.12 3:00pm, 腾讯会议】

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   2022-11-29 

  Colloquia & Seminars 

  

  Speaker

吴河辉,上海数学金沙娱app下载9570长聘副教授

  Title

Proper orientations and proper orientation number

  Time

12月12日15:00-16:00

  Venue

腾讯会议ID:682-358-567

  Abstract

  The proper orientation number \Vec{\chi}(G) of a graph G is the minimum k such that there exists an orientation of the edges of G with all vertex-outdegrees at most k and such that for any adjacent vertices, the outdegrees are different. Two major conjectures about the proper orientation number are resolved. First it is shown, that \Vec{\chi}(G) of any planar graph G is  at most 14. Secondly, it is shown that for every graph, \Vec{\chi}(G) is at most O(\frac{r\log r}{\log\log r})+\tfrac{1}{2}\MAD(G), where r=\chi(G) is the usual chromatic number of the graph, and \MAD(G) is the maximum average degree taken over all subgraphs of G. Several other related results are derived. Our proofs are based on a novel notion of fractional orientations. This is joint work with Professor Bojan Mohar and my student Yaobin Chen. 

  Affiliation

  吴河辉,现为上海数学金沙娱app下载9570长聘副教授,2011年获得美国伊利诺伊大学博士学位,导师为国际著名的图论专家Douglas B. West教授;2014年入选国家高层次人才计划,2019年入选上海市曙光学者,同年作为首位中国学者受邀在欧洲组合大会做大会报告。从2022年开始任J. Comb. Optimization杂志副编委。在结构图论,极值组合证明了包括Fouquet-Jolivet 猜想,Ohba猜想,Seymour等人的出邻域染色猜想,以及Kalai-Meshulam猜想等数学难题。多篇文章被JEMS, JCTB, Combinatorica, Forum Math-Sigma等数学著名期刊发表或接收。

  

  

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