Associated primes of powers of edge ideals and ear decompositions of graphs

Abstract

In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between two seemingly unrelated notions of Commutative Algebra and Combinatorics. It covers all previous major results in this topic and has several interesting consequences.

arXiv comment28 pages, 7 figures. This revision contains more comments on the methods and the results of the paper. Important terminology and notations now appear in Definition environments for the convenience of the readers. That changes the numeration of the results considerably. This paper will appear in Trans. Amer. Math. Soc

References in corpus (5)

• Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
• Stability of Depths of Powers of Edge Ideals
• Bounding the socles of powers of squarefree monomial ideals
• Stability of associated primes of monomial ideals
• Combinatorial characterizations of the saturation and the associated primes of the fourth power of edge ideals

Cited by in corpus (5)

• Symbolic powers of edge ideals of graphs
• Stabilization of associated prime ideals of monomial ideals -- Bounding the copersistence index
• The socle module of a monomial ideal
• Depth stability of edge ideals
• Saturation degree of powers of graded ideals