4 papers
Chen-Chvátal Conjecture for Graphs of Diameter 3
MartÃn Matamala, Luciano Villarroel-Sepúlveda
In 2008, Chen and Chvátal conjectured that in every finite metric space of points, there are at least distinct lines, or the whole set of points is a line. This is a gener…
A characterization of graphs of diameter two with fewer lines than vertices
MartÃn Matamala
In 2008 Chen and Chvátal conjectured that any metric space on n points has at least n lines, unless all the points belong to one line. Chv\atal proved in 2014 that this is indeed…
A characterization of locally ordered ternary relations in terms of digraphs
Guillermo Gamboa Quintero, MartÃn 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…
Locally connected graphs: metric properties
MartÃn Matamala, Juan Pablo Peña, José Zamora
In this work we show that any connected locally connected graph defines a metric space having at least as many lines as vertices with only three exception: the complete multipartit…