Details:
Title  Ideals and graphs, Gröbner bases and decision procedures in graphs  Author(s)  Giuseppa Carrà Ferro, Daniela Ferrarello  Type  Article in Journal  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  ISSN  0012365X 
URL 
http://www.sciencedirect.com/science/article/pii/S0012365X07003688 
Language  English  Journal  Discrete Mathematics  Volume  308  Number  2–3  Pages  287  298  Year  2008  Note  Combinatorics04Discrete and Combinatorial Mathematics  Edition  0  Translation 
No  Refereed 
No 
