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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.

Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity