Resumen de Regularity of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari

• 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 ?(?)(?) is its k-th symbolic power. We prove that ?deg(?(?))≤reg(?(?)(?))≤(?−1)deg(?(?))+|?(?)|−1.

  We also determine families of graphs for which the above inequalities are equality.