Author, as appears in the article.: Alberto Rodriguez-Velazquez, Juan
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Rodríguez Velázquez, Juan Alberto
Keywords: Metric space Lexicographic metric space De bruijn-erdos theorem De bruijn-erd?s theorem Corona metric space Chen-chvatal conjecture
Abstract: In a metric space (X, d), a line induced by two distinct points x, x' is an element of X, denoted by {x pound, x'}, is the set of points given by{x pound, x'} = {z is an element of X : d(x, x') = d(x, z) + d(z, x') or d(x, x') = |d(x, z) - d(z, x')|}.A line {x pound, x'} is universal whenever {x pound, x'} = X.Chen and Chvatal [Discrete Appl. Math. 156 (2008), 2101-2108.] conjectured that every finite metric space on n >= 2 points either has at least n distinct lines or has a universal line. In this paper, we prove this conjecture for some classes of metric spaces.In particular, we discuss the classes of Cartesian metric spaces, lexicographic metric spaces and corona metric spaces.
Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: juanalberto.rodriguez@urv.cat
Author identifier: 0000-0002-9082-7647
Record's date: 2024-10-26
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: http://www.aimspress.com/article/doi/10.3934/math.2021452
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Aims Mathematics. 6 (7): 7766-7781
APA: Alberto Rodriguez-Velazquez, Juan (2021). Solution of the Chen-Chvatal conjecture for specific classes of metric spaces. Aims Mathematics, 6(7), 7766-7781. DOI: 10.3934/math.2021452
Article's DOI: 10.3934/math.2021452
Entity: Universitat Rovira i Virgili
Journal publication year: 2021
Publication Type: Journal Publications
Repositori URV