2000 character limit reached
Spanning trees and continued fractions (2411.18782v2)
Published 27 Nov 2024 in math.CO and math.NT
Abstract: We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on $n$ 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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.