On the number of spanning trees in random regular graphs
Greenhill C, Kwan MA, Wind D. 2014. On the number of spanning trees in random regular graphs. The Electronic Journal of Combinatorics. 21(1), P1.45.
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Author
Greenhill, Catherine;
Kwan, Matthew AlanISTA 
;
Wind, David
;
Wind, DavidAbstract
Let d≥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→∞, 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.
Publishing Year
Date Published
2014-02-28
Journal Title
The Electronic Journal of Combinatorics
Volume
21
Issue
1
Article Number
P1.45
eISSN
IST-REx-ID
Cite this
Greenhill C, Kwan MA, Wind D. On the number of spanning trees in random regular graphs. The Electronic Journal of Combinatorics. 2014;21(1). doi:10.37236/3752
Greenhill, C., Kwan, M. A., & Wind, D. (2014). On the number of spanning trees in random regular graphs. The Electronic Journal of Combinatorics. The Electronic Journal of Combinatorics. https://doi.org/10.37236/3752
Greenhill, Catherine, Matthew Alan Kwan, and David Wind. “On the Number of Spanning Trees in Random Regular Graphs.” The Electronic Journal of Combinatorics. The Electronic Journal of Combinatorics, 2014. https://doi.org/10.37236/3752.
C. Greenhill, M. A. Kwan, and D. Wind, “On the number of spanning trees in random regular graphs,” The Electronic Journal of Combinatorics, vol. 21, no. 1. The Electronic Journal of Combinatorics, 2014.
Greenhill C, Kwan MA, Wind D. 2014. On the number of spanning trees in random regular graphs. The Electronic Journal of Combinatorics. 21(1), P1.45.
Greenhill, Catherine, et al. “On the Number of Spanning Trees in Random Regular Graphs.” The Electronic Journal of Combinatorics, vol. 21, no. 1, P1.45, The Electronic Journal of Combinatorics, 2014, doi:10.37236/3752.
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