Article

Archiv der Mathematik

, 93:451

First online:

Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity

  • Adam Van TuylAffiliated withDepartment of Mathematical Sciences, Lakehead University Email author 

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Abstract

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.

Mathematics Subject Classification (2000)

13F55 13D02 05C75

Keywords

Sequentially Cohen–Macaulay Edge ideals Bipartite graphs Vertex decomposable Shellable complex Castelnuovo–Mumford regularity