Carlos E. Valencia

Learn More
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)
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)
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)
  • 1