Proximity graphs

E, δ, Δ, χ and ω

Prosenjit Bose, Vida Dujmović, Ferran Hurtado, John Iacono, Stefan Langerman, Henk Meijer, Vera Sacristán, Maria Saumell, David R. Wood

    Research output: Contribution to journalArticle

    Abstract

    Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and give bounds on the same parameters.

    Original languageEnglish (US)
    Pages (from-to)439-469
    Number of pages31
    JournalInternational Journal of Computational Geometry and Applications
    Volume22
    Issue number5
    DOIs
    StatePublished - Oct 2012

    Fingerprint

    Proximity Graphs
    Graph in graph theory
    Clique number
    Delaunay
    Minimum Degree
    Chromatic number
    Maximum Degree
    Point Sets
    Higher Order

    Keywords

    • Geometric graphs
    • graph-theoretic properties
    • proximity graphs

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Applied Mathematics
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Bose, P., Dujmović, V., Hurtado, F., Iacono, J., Langerman, S., Meijer, H., ... Wood, D. R. (2012). Proximity graphs: E, δ, Δ, χ and ω. International Journal of Computational Geometry and Applications, 22(5), 439-469. https://doi.org/10.1142/S0218195912500112

    Proximity graphs : E, δ, Δ, χ and ω. / Bose, Prosenjit; Dujmović, Vida; Hurtado, Ferran; Iacono, John; Langerman, Stefan; Meijer, Henk; Sacristán, Vera; Saumell, Maria; Wood, David R.

    In: International Journal of Computational Geometry and Applications, Vol. 22, No. 5, 10.2012, p. 439-469.

    Research output: Contribution to journalArticle

    Bose, P, Dujmović, V, Hurtado, F, Iacono, J, Langerman, S, Meijer, H, Sacristán, V, Saumell, M & Wood, DR 2012, 'Proximity graphs: E, δ, Δ, χ and ω', International Journal of Computational Geometry and Applications, vol. 22, no. 5, pp. 439-469. https://doi.org/10.1142/S0218195912500112
    Bose P, Dujmović V, Hurtado F, Iacono J, Langerman S, Meijer H et al. Proximity graphs: E, δ, Δ, χ and ω. International Journal of Computational Geometry and Applications. 2012 Oct;22(5):439-469. https://doi.org/10.1142/S0218195912500112
    Bose, Prosenjit ; Dujmović, Vida ; Hurtado, Ferran ; Iacono, John ; Langerman, Stefan ; Meijer, Henk ; Sacristán, Vera ; Saumell, Maria ; Wood, David R. / Proximity graphs : E, δ, Δ, χ and ω. In: International Journal of Computational Geometry and Applications. 2012 ; Vol. 22, No. 5. pp. 439-469.
    @article{74184c88b8a94ae582b8a50cdf2c0e14,
    title = "Proximity graphs: E, δ, Δ, χ and ω",
    abstract = "Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and give bounds on the same parameters.",
    keywords = "Geometric graphs, graph-theoretic properties, proximity graphs",
    author = "Prosenjit Bose and Vida Dujmović and Ferran Hurtado and John Iacono and Stefan Langerman and Henk Meijer and Vera Sacrist{\'a}n and Maria Saumell and Wood, {David R.}",
    year = "2012",
    month = "10",
    doi = "10.1142/S0218195912500112",
    language = "English (US)",
    volume = "22",
    pages = "439--469",
    journal = "International Journal of Computational Geometry and Applications",
    issn = "0218-1959",
    publisher = "World Scientific Publishing Co. Pte Ltd",
    number = "5",

    }

    TY - JOUR

    T1 - Proximity graphs

    T2 - E, δ, Δ, χ and ω

    AU - Bose, Prosenjit

    AU - Dujmović, Vida

    AU - Hurtado, Ferran

    AU - Iacono, John

    AU - Langerman, Stefan

    AU - Meijer, Henk

    AU - Sacristán, Vera

    AU - Saumell, Maria

    AU - Wood, David R.

    PY - 2012/10

    Y1 - 2012/10

    N2 - Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and give bounds on the same parameters.

    AB - Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and give bounds on the same parameters.

    KW - Geometric graphs

    KW - graph-theoretic properties

    KW - proximity graphs

    UR - http://www.scopus.com/inward/record.url?scp=84874035162&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84874035162&partnerID=8YFLogxK

    U2 - 10.1142/S0218195912500112

    DO - 10.1142/S0218195912500112

    M3 - Article

    VL - 22

    SP - 439

    EP - 469

    JO - International Journal of Computational Geometry and Applications

    JF - International Journal of Computational Geometry and Applications

    SN - 0218-1959

    IS - 5

    ER -