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

摘要

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