图论中的计数理论及其应用

Graph-based counting theory and its applications

随着信息科学的迅速发展,研究离散对象的图论及组合数学正扮演着越来越重要的角色,其中基于图的各种计数理论在统计物理、分析化学及信息生物学等领域得到了很好的应用.本文综述了以张福基教授为代表的厦门大学组合图论研究团队20多年来在图论的计数理论及其应用方面的研究,主要包括匹配计数、组合计数、组合纽结、随机图、网络优化以及相关应用方面取得的成果,并提出未来研究的展望.

Due to the rapid development of information science,graph theory and combinatorics have played an increasingly important role in the study of discrete objects.Led by professor Fuji Zhang,the research team of combinatorics and graph theory of Xiamen University has devoted itself to the study of graph-based counting theory and applications in statistic physics and analytical?chemistry for a long time.During this time,the team adheres to the problem-oriented and application-driven approach.In this paper,we survey the main work conducted by the team in past two decades,including matching theory,combinatorial enumeration,topological graph theory,combinatorial knot theory,random graph theory,network optimization and related applications.