5 papers
A characterization of locally ordered ternary relations in terms of digraphs
Guillermo Gamboa Quintero, Martín Matamala, Juan Pablo Peña
In 1917, Huntington and Kline, followed by Huntington in 1924, studied systems of axioms for ternary relations aiming to capture the concepts of linear order (called betwenness) an…
Minimum blocking sets for families of partitions
Guillermo Gamboa Quintero, Ida Kantor
A -partition of an -element set is a triple of pairwise disjoint nonempty subsets such that . We determine the minimum size of a set $\m…
Quasimetric spaces with few lines
Guillermo Gamboa Quintero, Martín Matamala, Juan Pablo Peña
Chen and Chvátal conjectured in 2008 that in any finite metric space either there is a line containing all the points - a universal line -, or the number of lines is at least the n…
Metric Spaces in Which Many Triangles Are Degenerate
Vašek Chvátal, Noé de Rancourt, Guillermo Gamboa Quintero +2
Richmond and Richmond (American Mathematical Monthly 104 (1997), 713--719) proved the following theorem: If, in a metric space with at least five points, all triangles are degenera…
Sparse metric hypergraphs
Vašek Chvátal, Guillermo A. Gamboa Quintero., Ida Kantor
Given a metric space , we say is between and if . A metric space gives rise to a 3-uniform hypergraph that has as hyperedges those tri…