## Involve: A Journal of Mathematics

- Involve
- Volume 4, Number 3 (2011), 263-270.

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

Kim Kesting, James Pozzi, and Janet Striuli

#### 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.

#### Article information

**Source**

Involve, Volume 4, Number 3 (2011), 263-270.

**Dates**

Received: 26 September 2010

Revised: 20 January 2011

Accepted: 21 January 2011

First available in Project Euclid: 20 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.involve/1513733396

**Digital Object Identifier**

doi:10.2140/involve.2011.4.263

**Mathematical Reviews number (MathSciNet)**

MR2905227

**Zentralblatt MATH identifier**

1245.05063

**Subjects**

Primary: 00A05: General mathematics

**Keywords**

graph polynomial ring cover ideal associated prime ideals

#### Citation

Kesting, Kim; Pozzi, James; Striuli, Janet. On the associated primes of the third power of the cover ideal. Involve 4 (2011), no. 3, 263--270. doi:10.2140/involve.2011.4.263. https://projecteuclid.org/euclid.involve/1513733396