Saturation and associated primes of powers of edge ideals

2014/11/28 by Hien, Ha Thi Thu, Lam, Ha Minh, Trung, Ngo Viet · 1 citation
#13C05 #13F55 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.7740

Abstract

For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded associated primes of a power of I as covers of G which contain certain types of subgraphs of G. As an application, we completely classify the associated primes of the second and the third power of I in terms of G.

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• Associated primes of the second power of closed neighborhood ideals of graphs

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