Spanning trees and continued fractions
Combinatorics
2025-07-02 v2 Number Theory
Abstract
We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on vertices, answering a question of Sedl\'a\v{c}ek from 1969. The proof uses a connection with continued fractions, ``thin orbits,'' and Zaremba's conjecture.
Cite
@article{arxiv.2411.18782,
title = {Spanning trees and continued fractions},
author = {Swee Hong Chan and Alex Kontorovich and Igor Pak},
journal= {arXiv preprint arXiv:2411.18782},
year = {2025}
}
Comments
21 pages, 7 figures. New references are added to v2