Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity Academic Article uri icon

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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.

publication date

  • November 2009