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arXiv · 1707.05440

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
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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).

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Oswin Aichholzer, Thomas Hackl, Matias Korman, Marc van Kreveld, Maarten Löffler, Alexander Pilz, Bettina Speckmann, Emo Welzl. 2017-07-18. Packing Plane Spanning Trees and Paths in Complete Geometric Graphs. https://doi.org/10.1016/j.ipl.2017.04.006

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