Complete forcing numbers of graphs
数学公众报告(120周年校庆系列第97场)
报告题目(Title)：Complete forcing numbers of graphs
报告人(Speaker)：张和平 教授 (兰州大学)
地点(Place)：腾讯会议 ID：412 679 921
时间(Time)：2023 年 4 月 28 日(周五), 16:30-17:30
邀请人(Inviter)：徐敏
报告摘要
The complete forcing number of a graph G is the minimum cardinality of an edge subset of G on which the restriction of each perfect matching M is a forcing set of M. This concept can be view as not only a strengthening of the concept of global forcing number of G, but also a combination of forcing and anti-forcing of each perfect matching of G. This talk will present some progresses on this topic: We gave a tight upper bound on the complete forcing number of a hexagonal system in terms of elementary edge-cut cover; By an elementary edge-cut decomposition we obtained that the complete forcing number of a graph is no more than 2 times its cyclomatic number and characterized the matching covered graphs whose complete forcing numbers attain this upper bound and this upper bound minus 1 respectively; We obtained formulas for the complete forcing number of some types of graphs, such as wheels, grid cylinders, normal hexagonal systems without 2×3 subsystems, parallelogram, regular hexagon- and rectangle-shaped hexagonal systems, complete multipartite graphs and some edge-deleted subgraphs; For a (4,6)-fullerene graph, we have obtained that the complete forcing number is equal to or larger than the Clar number plus the Fries number, and conjectured the equality always holds. This is a joint work with Dr. Xin He.
主讲人简介
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），2014年6月当选国际数学化学科学院院士（Member of the International Academy of Mathematical Chemistry）。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、化学图论和计算机网络的研究，发表了200余篇SCI 收录学术论文，主持了国家自然科学基金项目8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。
