Vol. 4, No. 3, 2011

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ISSN: 1944-4184 (e-only)
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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
Mathematical Subject Classification 2010
Primary: 00A05
Milestones
Received: 26 September 2010
Revised: 20 January 2011
Accepted: 21 January 2011
Published: 13 March 2012

Communicated by Joseph Gallian
Authors
Kim Kesting
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06824
United States
James Pozzi
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06824
United States
Janet Striuli
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06824
United States