[1]唐保祥,任 韩.4类特殊图完美匹配的计数[J].南京师大学报(自然科学版),2013,36(01):10-15.
　Tang Baoxiang,Ren Han.The Number of Perfect Matchings in Four Types of Particular Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):10-15.
点击复制

4类特殊图完美匹配的计数()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年01期
页码:
10-15
栏目:
数学
出版日期:
2013-03-31

文章信息/Info

Title:
The Number of Perfect Matchings in Four Types of Particular Graphs
作者:
唐保祥1; 任 韩2
(1.天水师范学院数学与统计学院,甘肃 天水 741001) (2.华东师范大学数学系,上海 200062)
Author(s):
Tang Baoxiang1; Ren Han2
(1.School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,China) (2.Department of Mathematics,East China Normal University,Shanghai 200062,China)
关键词:
完美匹配; 线性递推式; 特征方程
Keywords:
perfect matching; linear recurrence relation; characteristic equation
分类号:
O157.5
摘要:
匹配计数理论是图论的核心内容之一,由于得到应用领域的支持,并与其他理论课题发生密切联系,受到众多学者的关注,产生出许多含义丰富而深刻的理论成果.但是,一般图的完美匹配计数问题却是NP-难问题.本文用划分、求和、再嵌套递推的方法给出了4类图完美匹配数目的显式表达式,所给出的方法,可以计算出许多特殊图的所有完美匹配的数目.
Abstract:
Matching counting theory is at the core of graph theory.Since it has important applications and is in connection with other theoretic problems closely,it has been studied extensively,and many celebrated results have been established.But the problem of counting the number of perfect matchings for general graphs is NP-hard.In this paper,by applying differentiation,summation and re-nested recursive calculation,several counting formulas of the perfect matching for four specific types of graphs are given.By the method presented in this paper,the number of all perfect matchings of many particular graphs can be calculated.

参考文献/References:

[1] Kasteleyn P W.Graph Theory and Crystal Physics[M].Harary F.Graph Theory and Theoretical Physics.London:Academic Press,1967:43-110.
[2]Hall G G.A graphic model of a class of molecules[J].Int J Math Edu Sci Technol,1973,4(3):233-240.
[3]Cyvin S J,Gutman I.Keku｀Structures in Benzennoid Hydrocarbons[M].Berlin:Springer Press,1988.
[4]Ciucu M.Enumeration of perfect matchings in graphs with reflective symmetry[J].J Combin Theory Ser A,1997,77:87-97.
[5]Fischer I,Little C H C.Even circuits of prescribed clockwise parity[J].Electro J Combin,2003,10:1-20.
[6]Jockusch W.Perfect mathings and perfect squares[J].J Combin Theory Ser A,1994,67:100-115.
[7]Kasteleyn P W.Dimmer statistics and phase transition[J].Journal of Mathematical Physics,1963,4:287-293.
[8]Lovász L,Plummer M.Matching Theory[M].New York:North-Holland Press,1986.
[9]于青林,刘桂真.图的因子和匹配可扩性[M].北京:高等教育出版社,2010.
[10]Zhang Heping.The connectivity of ansformation graphs of perfect matchings of polyominoes[J].Discrete Mathematics,1996,158:257-272.
[11]Zhang Heping,Zhang Fuji.Perfect matchings of polyomino graphs[J].Graphs and Combinatorics,1997,13:259-304.
[12]张莲珠.渺位四角系统完美匹配数的计算[J].厦门大学学报:自然科学版,1998,37(5):629-633.
[13]林泓,林晓霞.若干四角系统完美匹配数的计算[J].福州大学学报:自然科学版,2005,33(6):704-710.
[14]Yan Weigen,Zhang Fuji.Enumeration of perfect matchings of a type of Cartesian products of graphs[J].Discrete Applied Mathematics,2006,154:145-157.
[15]唐保祥,任韩.几类图完美匹配的数目[J].南京师大学报:自然科学版,2010,33(3):1-6.
[16]唐保祥,李刚,任韩.3类图完美匹配的数目[J].浙江大学学报:理学版,2011,38(4):16-19.
[17]唐保祥,任韩.2类图完美匹配的数目[J].西南师范大学学报:自然科学版,2011,36(5):16-21.
[18]唐保祥,任韩.3类图完美匹配的计数[J].南京师大学报:自然科学版,2012,35(1):16-21.
[19]唐保祥,任韩.6类图完美匹配的数目[J].中山大学学报:自然科学版,2012,51(1):40-44.

相似文献/References:

[1]唐保祥,任韩.3类图完美匹配的计数[J].南京师大学报(自然科学版),2012,35(01):16.
　Tang Baoxiang,Ren Han.The Number of Perfect Matchings in Three Types of Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(01):16.
[2]唐保祥.几类图完美匹配的数目[J].南京师大学报(自然科学版),2010,33(03):1.
　Tang Baoxiang,Ren Han.The Number of Perfect Matching in Several Types of Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(01):1.
[3]唐保祥,任　韩.3类3-正则图中的完美对集数[J].南京师大学报(自然科学版),2016,39(01):21.
　Tang Baoxiang,Ren Han.The Number of Perfect Matchings in Two Types of 3-Regular Graph[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(01):21.
[4]唐保祥,任 韩.2类图的完美匹配数的分类递推求法[J].南京师大学报(自然科学版),2019,42(01):1.[doi:10.3969/j.issn.1001-4616.2019.01.001]
　Tang Baoxiang,Ren Han.Classification and Push Solution Method for the Number ofPerfect Matchings of Two Types Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(01):1.[doi:10.3969/j.issn.1001-4616.2019.01.001]
[5]唐保祥,任 韩.3类图完美匹配数目的计算公式[J].南京师大学报(自然科学版),2016,39(04):0.[doi:10.3969/j.issn.1001-4616.2016.04.001]
　Tang Baoxiang,Ren Han.Counting Formulas of the Number of Perfect Matchings ofthe Three Types of Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(01):0.[doi:10.3969/j.issn.1001-4616.2016.04.001]
[6]唐保祥,任韩.2类图完美匹配数目解析式的嵌套递推求法[J].南京师大学报(自然科学版),2020,43(01):1.[doi:10.3969/j.issn.1001-4616.2020.01.001]
　TangBaoxiang,RenHan.TheNestedRecursiveMethodofAnalyticFormulaoftheNumberofPerfectMatchingsforTwoTypesofGraphs[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(01):1.[doi:10.3969/j.issn.1001-4616.2020.01.001]

备注/Memo

备注/Memo:
收稿日期:2012-05-18.
基金项目:国家自然科学基金(11171114).
通讯联系人:唐保祥,副教授,研究方向:图论和组合数学.E-mail:tbx0618@sina.com
更新日期/Last Update: 2013-03-31