Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs
classification
🧮 math.AC
math.CO
keywords
edgebipartitebetticompletegraphidealidealssubgraphs
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Given a finite simple graph one can associate the edge ideal. In this paper we prove that a graded Betti number of the edge ideal does not vanish if the original graph contains a set of complete bipartite subgraphs with some conditions. Also we give a combinatorial description for the projective dimension of the edge ideals of unmixed bipartite graphs.
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