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res:
bibo_abstract:
- Let G be a graph on the vertex set V(G) = {x1,…,xn} with the edge set E(G), and
let R = K[x1,…, xn] be the polynomial ring over a field K. Two monomial ideals
are associated to G, the edge ideal I(G) generated by all monomials xixj with
{xi,xj} ∈ E(G), and the vertex cover ideal IG generated by monomials ∏xi∈Cxi for
all minimal vertex covers C of G. A minimal vertex cover of G is a subset C ⊂
V(G) 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 LG and we explicitly describe the minimal
free resolution of the ideal associated to LG 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Fatemeh
foaf_name: Mohammadi, Fatemeh
foaf_surname: Mohammadi
foaf_workInfoHomepage: http://www.librecat.org/personId=2C29581E-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Somayeh
foaf_name: Moradi, Somayeh
foaf_surname: Moradi
bibo_doi: 10.4134/BKMS.2015.52.3.977
bibo_issue: '3'
bibo_volume: 52
dct_date: 2015^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/2234-3016
dct_language: eng
dct_publisher: Korean Mathematical Society@
dct_title: Resolution of unmixed bipartite graphs@
...