[1]王小雯,郭 锦*.关于若干图类的复形余1维图实现问题研究[J].江西师范大学学报(自然科学版),2021,(04):335-338.[doi:10.16357/j.cnki.issn1000-5862.2021.04.02]
　WANG Xiaowen,GUO Jin*.The Study on the Realization of Codimension One Graph of Some Graphs by Simplicial Complexes[J].Journal of Jiangxi Normal University:Natural Science Edition,2021,(04):335-338.[doi:10.16357/j.cnki.issn1000-5862.2021.04.02]
点击复制

关于若干图类的复形余1维图实现问题研究()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2021年04期
页码:
335-338
栏目:
数学与应用数学
出版日期:
2021-08-10

文章信息/Info

Title:
The Study on the Realization of Codimension One Graph of Some Graphs by Simplicial Complexes
文章编号:
1000-5862(2021)03-0335-04
作者:
王小雯; 郭 锦*
海南大学理学院,海南 海口 570228
Author(s):
WANG Xiaowen; GUO Jin*
School of Science,Hainan University,Haikou Hainan 570228,China
关键词:
仙人掌图;  星三角形;  复形;  余1维图
Keywords:
cactus graph;  star triangle;  simplicial complex;  codimension one graph
分类号:
O 157.5
DOI:
10.16357/j.cnki.issn1000-5862.2021.04.02
文献标志码:
A
摘要:
该文对若干类图的复形余1维图实现的问题展开研究,证明了仙人掌图是可实现的,并给出了星三角形图(仙人掌图中的一小类)的一种实现方式.
Abstract:
The problem about the realizations of codimension one graph of simple graphs is studied.It is proved that all cactus graphs are realizable.A detailed realization is shown for the star triangle graph,which is a kind of cactus graph.

参考文献/References:

[1] Van Tuyl A,Villarreal R H.Shellable graphs and sequentially Cohen-Macaulay bipartite graphs [J].Journal of Combinatorial Theoory:Series A,2008,115(5):799-814.
[2] Björner A.Shellable and Cohen-Macaulay partially ordered sets [J].Transactions of the American Mathematical Society,1980,260(1):159-183.
[3] Herzog J,Hibi T,Zheng Xinxian.Cohen-Macaulay chordal graphs [J].Journal of Combinatorial Theoory:Series A,2006,113(5):911-916.
[4] Stanley R P.Combinatorics and commutative algebra [M].2nd ed.Boston,Basel,Berlin:Birkhäuser,1996.
[5] Villarreal R H.Cohen-Macaulay graphs [J].Manuscripta Mathematica,1990,66(1):277-293.
[6] Guo Jin,Shen Yihuang,Wu Tongsuo.Strong shellability of simplicial complexes [J].Journal of the Korean Mathematical Society,2019,56(6):1613-1639.
[7] 郭锦,李海燕.关于余一维图的实现的研究 [J].海南大学学报:自然科学版,2017,35(1):7-10.
[8] Mohammadi F,Kiani D,Yassemi S.Shellable cactus graphs [J].Mathematica Scandinavica,2010,106(2):161-168.
[9] Baste J,Gözüpek D,Paul C,et al.Parameterized complexity of finding a spanning tree with minimum reload cost diameter [J].Network.2020,75(3):259-277.
[10] Nishi T,Chua L O.Topological criteria for nonlinear resistive circuits containing controlled sources to have a unique solution [J].IEEE Transactions on Circuits and Systems,1984,31(8):722-741.
[11] Arcak M.Diagonal stability on cactus graphs and application to network stability analysis [J].IEEE Transactions on Automatic Control,2011,56(12):2766-2777.
[12] Paten B,Diekhans M,Earl D,et al.Cactus graphs for genome comparisons [J].Journal of Computational Biology,2011,18(3):469-481.
[13] Cameron K,Walker T.The graphs with maximum induced matching and maximum matching the same size [J].Discrete Mathematics,2015,299(1/2/3):49-55.
[14] Trung T N.Regularity,matchings and Cameron-Walker graphs [J].Collectanea Mathematica,2020,71(1):83-91.
[15] Hibi T,Higashitani A,Kimura K,et al.Algebraic study on Cameron-Walker graphs [J].Journal of Algebra,2015,422:257-269.
[16] Bolognini D,Macchia A,Strazzanti F.Binomial edge ideals of bipartite graphs [J].European Journal of Combinatorics,2018,70:1-25.

备注/Memo

备注/Memo:
收稿日期:2020-10-28
基金项目:国家自然科学基金(11961017),海南省自然科学基金(119MS002),海南省科协青年科技英才学术创新计划(QCXM201806)和海南省研究生创新科研课题(Hys2020-106)资助项目.
通信作者:郭 锦(1983—),男,湖南湘潭人,副教授,博士,主要从事组合交换代数研究.E-mail:guojinecho@163.com
更新日期/Last Update: 2021-08-10