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arXiv · 2505.16818

Spanning trees of bounded degree in random geometric graphs

Michael Anastos·Sahar Diskin·Dawid Ignasiak·Lyuben Lichev·Yetong Sha
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Abstract

We determine the sharp threshold for the containment of all $n$-vertex trees of bounded degree in random geometric graphs with $n$ vertices. This provides a geometric counterpart of Montgomery's threshold result for binomial random graphs, and confirms a conjecture of Espuny Díaz, Lichev, Mitsche, and Wesolek. Our proof is algorithmic and adapts to other families of graphs, in particular graphs with bounded genus or tree-width.

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Michael Anastos, Sahar Diskin, Dawid Ignasiak, Lyuben Lichev, Yetong Sha. 2025-05-22. Spanning trees of bounded degree in random geometric graphs. https://arxiv.org/abs/2505.16818

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