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International Workshop on Combinatorial Algorithms

IWOCA 2016: Combinatorial Algorithms pp 68–80Cite as

Plane Bichromatic Trees of Low Degree

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9843))

Abstract

Let R and B be two disjoint sets of points in the plane such that \(|B|\leqslant |R|\), and no three points of \(R\cup B\) are collinear. We show that the geometric complete bipartite graph \(\text {K(R,B)}\) contains a non-crossing spanning tree whose maximum degree is at most \(\max \left\{ 3, \left\lceil \frac{|R|-1}{|B|}\right\rceil + 1\right\} \); this is the best possible upper bound on the maximum degree. This solves an open problem posed by Abellanas et al. at the Graph Drawing Symposium, 1996.

Research supported by NSERC.

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Authors and Affiliations

  1. Carleton University, Ottawa, Canada

    Ahmad Biniaz, Prosenjit Bose, Anil Maheshwari & Michiel Smid

Authors
  1. Ahmad Biniaz
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  2. Prosenjit Bose
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  3. Anil Maheshwari
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  4. Michiel Smid
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Correspondence to Ahmad Biniaz .

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Editors and Affiliations

  1. University of Helsinki, Helsinki, Finland

    Veli Mäkinen

  2. University of Helsinki, Helsinki, Finland

    Simon J. Puglisi

  3. University of Helsinki, Helsinki, Finland

    Leena Salmela

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Biniaz, A., Bose, P., Maheshwari, A., Smid, M. (2016). Plane Bichromatic Trees of Low Degree. In: Mäkinen, V., Puglisi, S., Salmela, L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science(), vol 9843. Springer, Cham. https://doi.org/10.1007/978-3-319-44543-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-44543-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44542-7

  • Online ISBN: 978-3-319-44543-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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