Sharp threshold for embedding balanced spanning trees in random geometric graphs-Reference-Cited by-同舟云学术

Sharp threshold for embedding balanced spanning trees in random geometric graphs

Published:2023 Issue: Volume: Page:
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Container-title:Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications
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Author:

Díaz Alberto,Lichev Lyuben,Mitsche Dieter,Wesolek Alexandra

Abstract

Consider the random geometric graph $\mathcal{G}(n,r)$ obtained by independently assigning a uniformly random position in $[0,1]^2$ to each of the $n$ vertices of the graph and connecting two vertices by an edge whenever their Euclidean distance is at most $r$. We study the event that $\mathcal{G}(n,r)$ contains a spanning copy of a balanced tree $T$ and obtain sharp thresholds for these events. Our methods provide a polynomial-time algorithm for finding a copy of such trees $T$ above the threshold.

Publisher

Masaryk University Press

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1. Sharp threshold for embedding balanced spanning trees in random geometric graphs;Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications;2023