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On Geometric Graphs on Point Sets in the Plane

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Discrete and Computational Geometry, Graphs, and Games (JCDCGGG 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13034))

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Abstract

A graph whose vertex set is a set P of points in the plane and whose edges are line segments joining pairs of elements of P is called a geometric graph. In this paper we survey several results on geometric graphs on colored point sets. Of particular interest are bicolored point sets \(P= R \cup B\) in which the elements of P can considered to be colored red or blue. We will pay particular attention to perfect matchings, spanning trees and paths whose vertex sets are colored point sets. In the last section of this paper we give some results on point sets whose elements are labelled with the integers \(\{1, \ldots , n\}\) such that different elements of P receive different labels.

Research supported in part by PAPIIT grant IN102117 Universidad Nacional Autónoma de México.

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Acknowledgment

We would like to thank the referees for their careful reports.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Jorge Urrutia

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  1. Jorge Urrutia
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Correspondence to Jorge Urrutia .

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Editors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Jin Akiyama

  2. Ateneo de Manila University, Quezon City, Philippines

    Reginaldo M. Marcelo

  3. Ateneo de Manila University, Quezon City, Philippines

    Mari-Jo P. Ruiz

  4. Osaka Prefecture University, Osaka, Japan

    Yushi Uno

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Urrutia, J. (2021). On Geometric Graphs on Point Sets in the Plane. In: Akiyama, J., Marcelo, R.M., Ruiz, MJ.P., Uno, Y. (eds) Discrete and Computational Geometry, Graphs, and Games. JCDCGGG 2018. Lecture Notes in Computer Science(), vol 13034. Springer, Cham. https://doi.org/10.1007/978-3-030-90048-9_1

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  • DOI: https://doi.org/10.1007/978-3-030-90048-9_1

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