Spanning trees and continued fractions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866911030115827712 |
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| author | Chan, Swee Hong Kontorovich, Alex Pak, Igor |
| author_facet | Chan, Swee Hong Kontorovich, Alex Pak, Igor |
| contents | 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 Sedláček from 1969. The proof uses a connection with continued fractions, ``thin orbits,'' and Zaremba's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spanning trees and continued fractions Chan, Swee Hong Kontorovich, Alex Pak, Igor Combinatorics Number Theory 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 Sedláček from 1969. The proof uses a connection with continued fractions, ``thin orbits,'' and Zaremba's conjecture. |
| title | Spanning trees and continued fractions |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2411.18782 |