Regularity of symbolic powers of cover ideals of graphs

DOI10.1007/S13348-018-0228-8arXiv1709.03077WikidataQ129414704 ScholiaQ129414704MaRDI QIDQ6291096

Seyed Amin Seyed Fakhari

Publication date: 10 September 2017

Abstract: Let $G$ be a graph which belongs to either of the following classes: (i) bipartite graphs, (ii) unmixed graphs, or (iii) claw--free graphs. Assume that $J(G)$ is the cover ideal $G$ and $J(G{)}^{(k)}$ is its $k$-th symbolic power. We prove that${\displaystyle }$k{ m deg}(J(G))leq { m reg}(J(G)^{(k)})leq (k-1){ m deg}(J(G))+|V(G)|-1.${\displaystyle }$We also determine families of graphs for which the above inequalities are equality.

Mathematics Subject Classification ID

Algebraic combinatorics (05E99) Syzygies, resolutions, complexes and commutative rings (13D02)

This page was built for publication: Regularity of symbolic powers of cover ideals of graphs