Elsevier

Discrete Mathematics

Volume 308, Issues 2–3, 6 February 2008, Pages 287-298
Discrete Mathematics

Ideals and graphs, Gröbner bases and decision procedures in graphs☆

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Abstract

The well known correspondence between even cycles of an undirected graph and polynomials in a binomial ideal associated to a graph is extended to odd cycles and polynomials in another binomial ideal. Other binomial ideals associated to an undirected graph are also introduced. The results about them with topics on monomial ideals are used in order to show decision procedures for bipartite graphs, minimal vertex covers, cliques, edge covers and matchings with algebraic tools. All such procedures are implemented in Maple 9.5.

Keywords

Monomial and binomial ideal
Gröbner basis
Odd cycle
Bipartite graph

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The work has been supported by the project “Algebra Commutativa, Combinatorica e Computazionale 2005” of the Italian M.I.U.R.

Copyright © 2007 Published by Elsevier B.V.