Combinatorics of the integral closure of edge ideals related to n-partite graphs

Abstract

Combinatorial properties of some ideals related to n-partites graphs are examined. A description of the integral closure expressed through the log set of edge ideals of complete n-partite graphs is illustrated together with the fact that edge ideals of a strong quasi-n-partite graph are not integrally closed. Moreover, we are able to determine the structure and the invariants of the integral closure of the ideals of vertex covers for the edge ideals associated to a strong quasi-n-partite graph.