---
_id: '1547'
abstract:
- lang: eng
text: 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.
author:
- first_name: Fatemeh
full_name: Mohammadi, Fatemeh
id: 2C29581E-F248-11E8-B48F-1D18A9856A87
last_name: Mohammadi
- first_name: Somayeh
full_name: Moradi, Somayeh
last_name: Moradi
citation:
ama: Mohammadi F, Moradi S. Resolution of unmixed bipartite graphs. *Bulletin
of the Korean Mathematical Society*. 2015;52(3):977-986. doi:10.4134/BKMS.2015.52.3.977
apa: Mohammadi, F., & Moradi, S. (2015). Resolution of unmixed bipartite graphs.
*Bulletin of the Korean Mathematical Society*. Korean Mathematical Society.
https://doi.org/10.4134/BKMS.2015.52.3.977
chicago: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite
Graphs.” *Bulletin of the Korean Mathematical Society*. Korean Mathematical
Society, 2015. https://doi.org/10.4134/BKMS.2015.52.3.977.
ieee: F. Mohammadi and S. Moradi, “Resolution of unmixed bipartite graphs,” *Bulletin
of the Korean Mathematical Society*, vol. 52, no. 3. Korean Mathematical Society,
pp. 977–986, 2015.
ista: Mohammadi F, Moradi S. 2015. Resolution of unmixed bipartite graphs. Bulletin
of the Korean Mathematical Society. 52(3), 977–986.
mla: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite Graphs.”
*Bulletin of the Korean Mathematical Society*, vol. 52, no. 3, Korean Mathematical
Society, 2015, pp. 977–86, doi:10.4134/BKMS.2015.52.3.977.
short: F. Mohammadi, S. Moradi, Bulletin of the Korean Mathematical Society 52 (2015)
977–986.
date_created: 2018-12-11T11:52:39Z
date_published: 2015-05-31T00:00:00Z
date_updated: 2021-01-12T06:51:31Z
day: '31'
department:
- _id: CaUh
doi: 10.4134/BKMS.2015.52.3.977
intvolume: ' 52'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/0901.3015
month: '05'
oa: 1
oa_version: Preprint
page: 977 - 986
publication: Bulletin of the Korean Mathematical Society
publication_identifier:
eissn:
- 2234-3016
publication_status: published
publisher: Korean Mathematical Society
publist_id: '5624'
quality_controlled: '1'
scopus_import: 1
status: public
title: Resolution of unmixed bipartite graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2015'
...