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Betti splittings and multigraded Betti numbers of cover ideals of bipartite graphs (2312.08575v1)
Published 14 Dec 2023 in math.AC
Abstract: In this note, we study Betti splittings of cover ideals of bipartite graphs. We prove that if $J \subset \Bbbk [x_1,\dots,x_n]$ is the cover ideal of a bipartite graph then the $x_i$-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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