Betti splittings and multigraded Betti numbers of cover ideals of bipartite graphs
Abstract
In this note, we study Betti splittings of cover ideals of bipartite graphs. We prove that if J ⊂ [x1,…,xn] is the cover ideal of a bipartite graph then the xi-partition of J is a Betti splitting for any i. We also prove that multigraded Betti numbers of any squarefree monomial ideal can appear in a certain part of multigraded Betti numbers of the cover ideal of a bipartite graph.
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