Regularity of symbolic powers of cover ideals of graphs

2017/09/10 by Fakhari, S. A. Seyed
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.03077

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 thatk\rm deg(J(G))≤ \rm reg(J(G)^(k))≤ (k-1)\rm deg(J(G))+|V(G)|-1.We also determine families of graphs for which the above inequalities are equality.

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