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math.CO2024
Weighted Cages
G. Araujo-Pardo, C. De la Cruz, M. Matamala +1
Cages (-regular graphs of girth and minimum order) and their variants have been studied for over seventy years. Here we propose a new variant, "weighted cages". We character…
math.CO2024
Lines on digraphs of low diameter
Gabriela Araujo-Pardo, Martín Matamala, Juan P. Peña +1
A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvtal in 2008 conjectured that the same results is true in metric spaces for an…
math.CO2024
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…