Publisher DOI: 10.1016/j.aam.2015.12.001
Title: Spanning trees in random series-parallel graphs
Language: English
Authors: Ehrenmüller, Julia 
Rué, Juanjo 
Keywords: MSC primary 05A16;secondary 05C10
Issue Date: 1-Apr-2016
Source: Advances in Applied Mathematics (75): 18-55 (2016-04-01)
Abstract (english): 
By means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on n vertices chosen uniformly at random satisfies an estimate of the forms sρ-n(1+o(1)), where s and ρ are computable constants, the values of which are approximately s ≈ 0.09063 and ρ-1 ≈ 2.08415. We obtain analogous results for subfamilies of series-parallel graphs including 2-connected series-parallel graphs, 2-trees, and series-parallel graphs with fixed excess.
URI: http://hdl.handle.net/11420/5960
ISSN: 0196-8858
Institute: Mathematik E-10 
Document Type: Article
Journal: Advances in applied mathematics 
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