#### Vol. 4, No. 3, 2011

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On the associated primes of the third power of the cover ideal

### Kim Kesting, James Pozzi and Janet Striuli

Vol. 4 (2011), No. 3, 263–270
##### Abstract

An algebraic approach to graph theory involves the study of the edge ideal and the cover ideal of a given graph. While a lot is known for the associated primes of powers of the edge ideal, much less is known for the associated primes of the powers of the cover ideal. The associated primes of the cover ideal and its second power are completely determined. A configuration called a wheel is shown to always appear among the associated primes of the third power of the cover ideal.

##### Keywords
graph, polynomial ring, cover ideal, associated prime ideals
Primary: 00A05