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In this article, we discuss new characterizations of Cohen-Macaulay bipartite edge ideals. For arbitrary bipartite edge ideals I ( G ) , we also discuss methods to recognize regular elements on I ( G ) s for all s ≥ 1 in terms of the combinatorics of the graph G.

Cohen Macaulay Bipartite Graphs and Regular Element on the Powers of Bipartite Edge Ideals