Let $d\geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture.
@article{10_37236_3752,
author = {Catherine Greenhill and Matthew Kwan and David Wind},
title = {On the number of spanning trees in random regular graphs},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3752},
zbl = {1300.05283},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3752/}
}
TY - JOUR
AU - Catherine Greenhill
AU - Matthew Kwan
AU - David Wind
TI - On the number of spanning trees in random regular graphs
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3752/
DO - 10.37236/3752
ID - 10_37236_3752
ER -
%0 Journal Article
%A Catherine Greenhill
%A Matthew Kwan
%A David Wind
%T On the number of spanning trees in random regular graphs
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3752/
%R 10.37236/3752
%F 10_37236_3752
Catherine Greenhill; Matthew Kwan; David Wind. On the number of spanning trees in random regular graphs. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3752
