Regularity of symbolic powers of cover ideals of graphs

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 thatWe also determine families of graphs for which the above inequalities are equality.2000 Mathematics Subject Classification. Primary: 13D02, 05E99.