Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity

被引：0
作者：
Adam Van Tuyl
机构：
[1] Lakehead University,Department of Mathematical Sciences
来源：
Archiv der Mathematik | 2009年 / 93卷
关键词：
13F55; 13D02; 05C75; Sequentially Cohen–Macaulay; Edge ideals; Bipartite graphs; Vertex decomposable; Shellable complex; Castelnuovo–Mumford regularity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen–Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo–Mumford regularity of R/I(G) can be determined from the invariants of G.
引用
收藏
页码：451 / 459
页数：8
相关论文
共 32 条
[1]  
Björner A.(1996)Shellable nonpure complexes and posets. I Trans. Amer. Math. Soc. 348 1299-1327
[2]  
Wachs M.(1997)Shellable nonpure complexes and posets. II Trans. Amer. Math. Soc. 349 3945-3975
[3]  
Björner A.(2009)Algebraic properties of edge ideals via combinatorial topology Electron. J. Combin. 16 2-128
[4]  
Wachs M.(1997)Cohen–Macaulay bipartite graphs Arch. Math. 68 124-136
[5]  
Dochtermann A.(2004)Simplicial trees are sequentially Cohen–Macaulay J. Pure Appl. Algebra 190 121-316
[6]  
Engström A.(2008)Whiskers and sequentially Cohen–Macaulay graphs J. Combin. Theory Ser. A. 115 304-3282
[7]  
Estrada M.(2009)Splittings of monomial ideals Proc. Amer. Math. Soc. 137 3271-2337
[8]  
Villarreal R.H.(2007)Sequentially Cohen–Macaulay edge ideals Proc. Amer. Math. Soc. 135 2327-245
[9]  
Faridi S.(2008)Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers J. Algebraic Combin. 27 215-302
[10]  
Francisco C.A.(2005)Distributive lattices, bipartite graphs and Alexander duality J. Algebraic Combin. 22 289-960
1234