CIO and ring graphs: Deficiency and testing. (March 2017)

• Record Type: Journal Article
• Authors: Gitler, Isidoro; Reyes, Enrique; Vega, Juan A.
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 249
• Page End: 268
• Publication Date: 2017-03
• Subjects: Complete intersection toric ideals -- Oriented graphs -- Prisms -- Pyramids -- Thetas -- Ring graphs -- Chorded-thetas; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We give a polynomial time algorithm that tests whether a graph is a theta-ring graph or equivalently if a graph has the ∀ θ ∃ Δ -property (each chorded-theta has a transversal triangle). It is known that G is a theta-ring graph if and only if G is a CI O graph (each toric ideal associated to an edge orientation of G is a binomial complete intersection). In particular ring graphs are theta-ring graphs. We prove that the forbidden induced subgraphs that characterize ring graphs are chorded-thetas and K 4 . We introduce a new graph invariant, the CI O deficiency. This invariant has the property that graphs with CI O deficiency zero are exactly CI O graphs.