Regularity and projective dimension of the edge ideal of $C_5$-free vertex decomposable graphs
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Abstract:
In this paper, we explain the regularity, projective dimension and depth of the edge ideal of some classes of graphs in terms of invariants of graphs. We show that for a $C_5$-free vertex decomposable graph $G$, $\mbox {reg}(R/I(G))= c_G$, where $c_G$ is the maximum number of $3$-disjoint edges in $G$. Moreover, for this class of graphs we characterize $\mbox {pd}(R/I(G))$ and $\mbox {depth}(R/I(G))$. As a corollary we describe these invariants in forests and sequentially Cohen-Macaulay bipartite graphs.References
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Additional Information
- Fahimeh Khosh-Ahang
- Affiliation: Department of Mathematics, Ilam University, P. O. Box 69315-516, Ilam, Iran
- Email: fahime_khosh@yahoo.com
- Somayeh Moradi
- Affiliation: Department of Mathematics, Ilam University, P. O. Box 69315-516, Ilam, Iran; and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
- Email: somayeh.moradi1@gmail.com
- Received by editor(s): December 16, 2011
- Received by editor(s) in revised form: June 20, 2012
- Published electronically: February 17, 2014
- Communicated by: Irena Peeva
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 1567-1576
- MSC (2010): Primary 13D02, 13P10; Secondary 13D40, 13A02
- DOI: https://doi.org/10.1090/S0002-9939-2014-11906-X
- MathSciNet review: 3168464