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arXiv · 1306.1333

Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs

Kyouko Kimura
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Abstract

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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Kyouko Kimura. 2013-06-06. Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs. https://arxiv.org/abs/1306.1333

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