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- W2962682007 abstract "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 subgraph that is isomorphic to either H or a multipartite graph K2,...,2,a,b." @default.
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- W2962682007 date "2015-10-15" @default.
- W2962682007 modified "2023-09-24" @default.
- W2962682007 title "Betti numbers of subgraphs" @default.
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