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We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an effective method, based on the program Normaliz… (More)

- Carlos E. Valencia, Rafael H. Villarreal
- Eur. J. Comb.
- 2003

Let G be a connected bipartite graph. We present an approach to the computation of the canonical module of the edge subring associated to G using linear programming.

Let G be a graph without isolated vertices and let α(G) be its stability number and τ (G) its covering number. The σ v-cover number of a graph, denoted by σ v (G), is the maximum natural number m such that every vertex of G belongs to a maximal independent set with at least m vertices. In the first part of this paper we prove that α(G) ≤ τ (G)[1 + α(G) − σ… (More)

- Isidoro Gitler, Carlos E. Valencia
- Discrete Mathematics
- 2005

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge… (More)

- Carlos A. Alfaro, Burcu Aydin, Carlos E. Valencia, Elizabeth Bullitt, Alim Ladha
- Computational Statistics & Data Analysis
- 2014

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas to the more general space of rooted and labeled trees. We redefine concepts such as tree-line and forward principal… (More)

- Carlos E. Valencia, Marcos C. Vargas
- ArXiv
- 2014

Given an integer weighted bipartite graph {G = (U ⊔ V, E), w : E → Z} we consider the problems of finding all the edges that occur in some minimum weight matching of maximum cardinality and enumerating all the minimum weight perfect matchings. Moreover, we construct a subgraph Gcs of G which depends on an ǫ-optimal solution of the dual linear program… (More)

- Carlos A. Alfaro, Carlos E. Valencia
- Discrete Applied Mathematics
- 2014

- Carlos A. Alfaro, Carlos E. Valencia
- Electronic Notes in Discrete Mathematics
- 2015

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