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The average number of spanning trees in sparse graphs with given degrees

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Date

2017-06

Authors

Greenhill, Catherine
Isaev, Mikhail
Kwan, Matthew
McKay, Brendan D.

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence d = (d₁, . . . , dn), provided that the number of edges is at least n + 1/2d⁴max, where dmax is the maximum degree. A key part of our argument involves establishing a concentration result for a certain family of functions over random trees with given degrees, using Prüfer codes.

Description

Keywords

asymptotic, expression, random, graph, Prüfer, codes

Citation

URI

http://hdl.handle.net/1885/114488

Collections

ANU Research Publications

Source

European Journal of Combinatorics

Type

Journal article

Book Title

Entity type

Access Statement

Open Access

License Rights

DOI

10.1016/j.ejc.2017.02.003

Restricted until

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01 Greenhill et al The average number 2017.pdf (240.71 KB)

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