Plane Bichromatic Trees of Low Degree

  • Ahmad Biniaz
  • Prosenjit Bose
  • Anil Maheshwari
  • Michiel Smid
Conference paper

DOI: 10.1007/978-3-319-44543-4_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)
Cite this paper as:
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

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.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ahmad Biniaz
    • 1
  • Prosenjit Bose
    • 1
  • Anil Maheshwari
    • 1
  • Michiel Smid
    • 1
  1. 1.Carleton UniversityOttawaCanada

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