The diameter of the uniform spanning tree of dense graphs

The diameter of the uniform spanning tree of dense graphs

We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on n vertices with minimal degree linear in n is typically of order $\sqrt{n}$ . A byproduct of our proof, which is of independent interest, is that on such graphs the Cheeger constant and the spectral gap are c...

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Veröffentlicht in:Combinatorics, probability & computing probability & computing, 2022-11, Vol.31 (6), p.1010-1030
Hauptverfasser: Alon, Noga, Nachmias, Asaf, Shalev, Matan
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Apexes
Eigenvalues
Graph theory
Graphs
Markov analysis
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Zusammenfassung:We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on n vertices with minimal degree linear in n is typically of order $\sqrt{n}$ . A byproduct of our proof, which is of independent interest, is that on such graphs the Cheeger constant and the spectral gap are comparable.
ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548322000062