Regularity of Powers of edge ideal of very well-covered graphs

Pooran Norouzi; Seyed Amin Seyed Fakhari; Siamak Yassemi

Regularity of Powers of edge ideal of very well-covered graphs

Commutative Algebra 2017-07-19 v2 Combinatorics

Authors: Pooran Norouzi , Seyed Amin Seyed Fakhari , Siamak Yassemi

Abstract

Let $k\geq 3$ be an integer and $G$ be a very well-covered graph with ${\rm odd-girth}(G)\geq 2k+1$ . Assume that $I(G)$ is the edge ideal of $G$ . We show that for every integer $s$ with $1\leq s\leq k-2$ , we have ${\rm reg}(I(G)^s)=2s+\nu(G)-1$ , where $\nu (G)$ is the induced matching number of $G$ .

Keywords

edge ideal very well-covered graph regularity power of ideal induced matching number odd-girth

Cite

@article{arxiv.1707.04874,
  title  = {Regularity of Powers of edge ideal of very well-covered graphs},
  author = {Pooran Norouzi and Seyed Amin Seyed Fakhari and Siamak Yassemi},
  journal= {arXiv preprint arXiv:1707.04874},
  year   = {2017}
}

Related papers

View all related →