Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity

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Sequentially Cohen-macaulay Bipartite Graphs: Vertex Decomposability and Regularity

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.

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complement of special chordal graphs and vertex decomposability

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Shellable graphs and sequentially Cohen-Macaulay bipartite graphs

Associated to a simple undirected graph G is a simplicial complex ∆G whose faces correspond to the independent sets of G. We call a graph G shellable if ∆G is a shellable simplicial complex in the non-pure sense of Björner-Wachs. We are then interested in determining what families of graphs have the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we cla...

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ژورنال

عنوان ژورنال: Archiv der Mathematik

سال: 2009

ISSN: 0003-889X,1420-8938

DOI: 10.1007/s00013-009-0049-9