SPLITTINGS FOR SYMBOLIC POWERS OF EDGE IDEALS OF COMPLETE GRAPHS

Abstract

In this paper, we study the $s$-th symbolic powers of the edge ideals of complete graphs. In particular, we provide a criterion for finding an Eliahou–Kervaire splitting on these ideals, and we use the splitting to provide a description for the graded Betti numbers. We also discuss the symbolic powers and graded Betti numbers of edge ideals of parallelizations of finite simple graphs.