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TitleIdeals and graphs, Gröbner bases and decision procedures in graphs
Author(s) Giuseppa Carrà Ferro, Daniela Ferrarello
TypeArticle in Journal
AbstractThe 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.
KeywordsMonomial and binomial ideal, Gröbner basis, Odd cycle, Bipartite graph
ISSN0012-365X
URL http://www.sciencedirect.com/science/article/pii/S0012365X07003688
LanguageEnglish
JournalDiscrete Mathematics
Volume308
Number23
Pages287 - 298
Year2008
NoteCombinatorics04Discrete and Combinatorial Mathematics
Edition0
Translation No
Refereed No
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