Symbolic powers of cover ideal of very well-covered and bipartite graphs

2016/04/03 by Fakhari, S. A. Seyed · 2 citations
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00654

Abstract

Let G be a graph with n vertices and S=\mathbbK[x₁,…,x_n] be the polynomial ring in n variables over a field \mathbbK. Assume that J(G) is the cover ideal of G and J(G)^(k) is its k-th symbolic power. We prove that if G is a very well-covered graph such that J(G) has linear resolution, then J(G)^(k) has linear resolution, for every integer k≥ 1. We also prove that for a every very well-covered graph G, the depth of symbolic powers of J(G) forms a non-increasing sequence. Finally, we determine a linear upper bound for the regularity of powers of cover ideal of bipartite graph.

Cited by

• On the gradient of a monomial ideal
• The Serre depth of Stanley-Reisner rings and the depth of their symbolic powers

Related

• Symbolic powers of vertex cover ideals
• On the index of depth stability of symbolic powers of cover ideals of graphs
• Depth and Stanley depth of symbolic powers of cover ideals of graphs
• On the minimal free resolution of symbolic powers of cover ideals of\n graphs
• Regularity of symbolic powers of cover ideals of graphs