Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

Oswin Aichholzer; Thomas Hackl; Matias Korman; Marc van Kreveld; Maarten Löffler; Alexander Pilz; Bettina Speckmann; Emo Welzl

doi:10.1016/j.ipl.2017.04.006

Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

Computational Geometry 2017-07-19 v1

Authors: Oswin Aichholzer , Thomas Hackl , Matias Korman , Marc van Kreveld , Maarten Löffler , Alexander Pilz , Bettina Speckmann , Emo Welzl

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Abstract

We consider the following question: How many edge-disjoint plane spanning trees are contained in a complete geometric graph $GK_n$ on any set $S$ of $n$ points in general position in the plane? We show that this number is in $\Omega(\sqrt{n})$ . Further, we consider variants of this problem by bounding the diameter and the degree of the trees (in particular considering spanning paths).

Keywords

planar graph drawing

Cite

@article{arxiv.1707.05440,
  title  = {Packing Plane Spanning Trees and Paths in Complete Geometric Graphs},
  author = {Oswin Aichholzer and Thomas Hackl and Matias Korman and Marc van Kreveld and Maarten Löffler and Alexander Pilz and Bettina Speckmann and Emo Welzl},
  journal= {arXiv preprint arXiv:1707.05440},
  year   = {2017}
}

Comments

This work was presented at the 26th Canadian Conference on Computational Geometry (CCCG 2014), Halifax, Nova Scotia, Canada, 2014. The journal version appeared in Information Processing Letters, 124 (2017), 35--41

Packing Plane Spanning Trees and Paths in Complete Geometric Graphs

Abstract

Keywords

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