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Solution of the Chen-Chvatal conjecture for specific classes of metric spaces

  • Dades identificatives

    Identificador: imarina:9225163
    Handle: https://hdl.handle.net/20.500.11797/imarina9225163
    Autors:
    Alberto Rodriguez-Velazquez, Juan
    Resum:
    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.

  • Altres:

    Autor segons l'article: Alberto Rodriguez-Velazquez, Juan
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Rodríguez Velázquez, Juan Alberto
    Paraules clau: Metric space Lexicographic metric space De bruijn-erdos theorem De bruijn-erd?s theorem Corona metric space Chen-chvatal conjecture
    Resum: 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.
    Àrees temàtiques: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: juanalberto.rodriguez@urv.cat
    Identificador de l'autor: 0000-0002-9082-7647
    Data d'alta del registre: 2024-10-26
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: http://www.aimspress.com/article/doi/10.3934/math.2021452
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Aims Mathematics. 6 (7): 7766-7781
    Referència de l'ítem segons les normes 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
    DOI de l'article: 10.3934/math.2021452
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2021
    Tipus de publicació: Journal Publications

  • Paraules clau:

    Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Metric space
    Lexicographic metric space
    De bruijn-erdos theorem
    De bruijn-erd?s theorem
    Corona metric space
    Chen-chvatal conjecture
    Mathematics, applied
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    General mathematics

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