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Plane Bichromatic Trees of Low Degree

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Abstract

Let R and B be two disjoint sets of points in the plane such that \(|B|\le |R|\), and no three points of \(R\cup B\) are collinear. We show that the geometric complete bipartite graph K(R, B) contains a non-crossing spanning tree whose maximum degree is at most \(\max \,\{3, \lceil (|R|-1)/|B|\rceil + 1\}\); this is the best possible upper bound on the maximum degree. This proves two conjectures made by Kaneko, 1998, and solves an open problem posed by Abellanas et al. at the Graph Drawing Symposium, 1996.

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Acknowledgements

Research was supported by NSERC.

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Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Ahmad Biniaz, Prosenjit Bose, Anil Maheshwari & Michiel Smid

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  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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Editor in Charge: János Pach

A preliminary version of this paper has been accepted for presentation at 27th International Workshop on Combinatorial Algorithms (IWOCA), 2016.

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Biniaz, A., Bose, P., Maheshwari, A. et al. Plane Bichromatic Trees of Low Degree. Discrete Comput Geom 59, 864–885 (2018). https://doi.org/10.1007/s00454-017-9881-z

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  • DOI: https://doi.org/10.1007/s00454-017-9881-z

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