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数学研究所系列学术报告(张和平 兰州大学;王建锋 山东理工大学)

发布者:戴 情   发布时间:2021-12-21  浏览次数:170

报告题目1Relations between global forcing number and maximum anti-forcing number of a graph

报告专家张和平教授(兰州大学)

报告时间1223日周10:00-11:00

腾讯会议 672-904-984

报告摘要:The global forcing number of a graph G is the minimal cardinality of an edge subset discriminating all perfect matchings of G, denoted by gf (G). For a perfect matching M of G, the minimal number of edges not in M whose deletion results in a graph with a unique perfect matching is called the anti-forcing number of M. The maximum anti-forcing number of G among all perfect matchings is denoted by Af (G). It is known that the maximum anti-forcing number of a hexagonal system equals the famous Fries number. We report some comparisons between the global forcing number and the maximum anti-forcing number of a graph. For a bipartite graph G, we show that gf (G) ≥ Af (G). Next we mainly extend such result to some non-bipartite graphs. Let G be the set of all graphs with a perfect matching which contain no two disjoint odd cycles such that their deletion results in a subgraph with a perfect matching. For any GG, we also have gf (G) ≥ Af (G) by revealing further property of non-bipartite graphs with a unique perfect matching. As a consequence, this relation also holds for the graphs whose perfect matching polytopes consist of non-negative 1-regular vectors. In particular, for a brick G, de Carvalho, Lucchesi and Murty showed that GG if and only if G is solid, and if and only if its perfect matching polytope consists of non-negative 1-regular vectors. Finally, we give sharp lower and upper bounds on the difference gf (G) – Af (G).

专家简介: 张和平,兰州大学数学与统计学院教授(二级)、博士生导师,校学术委员会委员,院学术委员会主任。1994年获四川大学博士学位,1999年晋升教授,2001年任博士生导师,2001年获教育部第三届高校青年教师奖2002年获国务院颁发的政府特殊津贴,2009年入选甘肃省领军人才(2层次),20146月当选国际数学化学科学院院士(Member of the International Academy of Mathematical Chemistry)。曾任甘肃省数学会理事长,兰州大学数学与统计学院院长,中国数学会常务理事。现任中国组合数学与图论学会常务理事,中国运筹学会组合数学与图论分会常务理事。主要从事图的匹配理论和化学图论的研究,发表了180余篇SCI 收录学术论文,主持了国家自然科学基金项目7项,包括重点项目应用图论。曾在香港浸会大学,法国巴黎南大学,澳大利亚Newcastle大学,美国中田纳西州立大学,台湾中研院数学所学术访问。

 

报告题目2A Survey on Matrix Tree Theorem of Graphs

报告专家王建锋教授(山东理工大学

报告时间1223日周11:00-12:00

腾讯会议672-904-984

摘要: Kirchhoff's Matrix Tree Theorem gives the number of spanning trees in a connected graph by the determinant of a submatrix of the Laplacian. While, Tutte’s Matrix Tree Theorem is a generalization of the original Kirchhoff's Matrix Tree Theorem, which determines the number of spanning trees in a connected digraph. In the report, about this topic we summarize the related results and their methods used in the proofs. Particularly, we will introduce various extensions of Matrix Tree Theorem, which involves the signless Laplaician, Hermitian (quasi-)Laplacian matrix, signed Laplacian matrix and skew Laplacian matrix. Moreover, we generalize our result to the weighted digraphs.

 

专家简介王建锋,山东理工大学数学与统计学院教授、副院长,新疆大学博士、南开大学博士后,发表论文60余篇,现主持一项国家自然科学基金面上项目,主持完成国家自然科学基金2项,中国博士后科学基金和省级自然科学基金4项、参与完成3项国家自然科学基金。发表的部分结果被剑桥大学出版社和爱思唯尔(Elsevier出版社的专著收录。提出的问题得到荷兰、美国和韩国等知名图论专家的关注和彻底解决;应邀参加塞尔维亚第14届数学大会作邀请报告等。现任教育部学位中心通讯评议专家、中国博士后和北京等省市基金通讯评审专家, CSIAM信息和通讯领域的数学专委会委员。目前主要侧重于研究图谱理论、图多项式理论、图距离参数等方向。曾任中国科协九大代表、青海省昆仑英才计划科技创新领军人才、青海青年五四奖章等。

 

 

邀请人:数学研究所