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

  • Datos identificativos

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

  • Otros:

    Autor según el artículo: Alberto Rodriguez-Velazquez, Juan
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Rodríguez Velázquez, Juan Alberto
    Palabras clave: Metric space Lexicographic metric space De bruijn-erdos theorem De bruijn-erd?s theorem Corona metric space Chen-chvatal conjecture
    Resumen: 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.
    Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: juanalberto.rodriguez@urv.cat
    Identificador del autor: 0000-0002-9082-7647
    Fecha de alta del registro: 2024-10-26
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: http://www.aimspress.com/article/doi/10.3934/math.2021452
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Aims Mathematics. 6 (7): 7766-7781
    Referencia 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 del artículo: 10.3934/math.2021452
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2021
    Tipo de publicación: Journal Publications

  • Palabras clave:

    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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