Spanning trees of bounded degree in random geometric graphs
Combinatorics
2025-05-23 v1 Metric Geometry
Probability
Abstract
We determine the sharp threshold for the containment of all -vertex trees of bounded degree in random geometric graphs with vertices. This provides a geometric counterpart of Montgomery's threshold result for binomial random graphs, and confirms a conjecture of Espuny D\'iaz, Lichev, Mitsche, and Wesolek. Our proof is algorithmic and adapts to other families of graphs, in particular graphs with bounded genus or tree-width.
Keywords
Cite
@article{arxiv.2505.16818,
title = {Spanning trees of bounded degree in random geometric graphs},
author = {Michael Anastos and Sahar Diskin and Dawid Ignasiak and Lyuben Lichev and Yetong Sha},
journal= {arXiv preprint arXiv:2505.16818},
year = {2025}
}
Comments
10 pages