Plane Bichromatic Trees of Low Degree

  • Ahmad Biniaz
  • Prosenjit Bose
  • Anil Maheshwari
  • Michiel Smid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)


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.


Convex Hull Span Tree Maximum Degree Blue Point Blue Vertex 
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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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