Nonvanishing of Betti Numbers of Edge Ideals and Complete Bipartite Subgraphs
نویسندگان
چکیده
منابع مشابه
Bounding Betti Numbers of Bipartite Graph Ideals
We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs.
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Let G be a simple graph on n vertices. LetH be either the complete graph Km or the complete bipartite graph Kr,s on a subset of the vertices in G. We show that G contains H as a subgraph if and only if βi,α(H) ≤ βi,α(G) for all i ≥ 0 and α ∈ Z. In fact, it suffices to consider only the first syzygy module. In particular, we prove that β1,α(H) ≤ β1,α(G) for all α ∈ Z if and only if G contains a ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2015
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.984840