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RESOLUTION OF UNMIXED BIPARTITE GRAPHS
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 Title & Authors
RESOLUTION OF UNMIXED BIPARTITE GRAPHS
Mohammadi, Fatemeh; Moradi, Somayeh;
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 Abstract
Let G be a graph on the vertex set with the edge set E(G), and let be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials with , and the vertex cover ideal generated by monomials for all minimal vertex covers C of G. A minimal vertex cover of G is a subset such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers and we explicitly describe the minimal free resolution of the ideal associated to which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.
 Keywords
minimal free resolution;unmixed bipartite graph;edge ideal;
 Language
English
 Cited by
1.
THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH, Nagoya Mathematical Journal, 2017, 1  crossref(new windwow)
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