Codismantlability and projective dimension of the Stanley–Reisner ring of special hypergraphs
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In this paper, we generalize the concept of codismantlable graphs to hypergraphs and show that some special vertex decomposable hypergraphs are codismantlable. Then we generalize the concept of bouquet in graphs to hypergraphs to extend some combinatorial invariants of graphs about disjointness of a set of bouquets. We use these invariants to characterize the projective dimension of Stanley–Reisner ring of special hypergraphs in some sense.
KeywordsCodominated vertex edge ideal hypergraph matching number projective dimension vertex decomposable
2010 Mathematics Subject ClassificationPrimary: 13F55 13D05 Secondary: 05E45 05C65
The authors are very grateful to the referee for careful reading of the paper. The second author was in part supported by a grant from IPM (No. 94130021).
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