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A Balanced Interval of Two Sets of Points on a Line

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Combinatorial Geometry and Graph Theory (IJCCGGT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3330))

Abstract

Let n,m,k,h be positive integers such that 1 ≤ n ≤ m, 1≤ k ≤ n and 1≤ h ≤ m. Then we give a necessary and sufficient condition for a configuration with n red points and m blue points on a line to have an interval containing precisely k red points and h blue points.

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References

  1. Bárány, I., Matoušek, J.: Simultaneous partitions of measures by k-fans. Discrete Comput. Geom. 25, 317–334 (2001)

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  3. Kaneko, A., Kano, M.: Discrete geometry on red and blue points in the plane — A survey. In: Discrete and Computational GeometryE The Goodman-Pollack Festschrift, pp. 551–570. Springer, Heidelberg (2003)

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Author information

Authors and Affiliations

  1. Department of Computer Science and Communication Engineering, Kogakuin University, Nishi-Shinjuku, Shinjuku-ku, Tokyo, 163-8677, Japan

    Atsushi Kaneko

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan

    M. Kano

Authors
  1. Atsushi Kaneko
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  2. M. Kano
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokio, Japan

    Jin Akiyama

  2. Department of Mathematics, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung, P.O. Box, 40132, Indonesia

    Edy Tri Baskoro

  3. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

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© 2005 Springer-Verlag Berlin Heidelberg

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Kaneko, A., Kano, M. (2005). A Balanced Interval of Two Sets of Points on a Line. In: Akiyama, J., Baskoro, E.T., Kano, M. (eds) Combinatorial Geometry and Graph Theory. IJCCGGT 2003. Lecture Notes in Computer Science, vol 3330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30540-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-30540-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24401-1

  • Online ISBN: 978-3-540-30540-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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