Stochastic Embeddings of Graphs into Trees

Th. Schlumprecht; Garrett Tresch

Stochastic Embeddings of Graphs into Trees

Combinatorics 2023-06-13 v1 Metric Geometry

Authors: Th. Schlumprecht , Garrett Tresch

Abstract

It is known that every graph with n vertices embeds stochastically into trees with distortion $O(\log n)$ . In this paper, we show that this upper bound is sharp for a large class of graphs. As this class of graphs contains diamond graphs, this result extends known examples that obtain this largest possible stochastic distortion.

Keywords

graph theory random graphs spanning trees

Cite

@article{arxiv.2306.06222,
  title  = {Stochastic Embeddings of Graphs into Trees},
  author = {Th. Schlumprecht and Garrett Tresch},
  journal= {arXiv preprint arXiv:2306.06222},
  year   = {2023}
}