Non-planarity of Markoff graphs \(\mod p\)

DOI10.4171/cmh/566arXiv2105.12411OpenAlexW4391464321MaRDI QIDQ6204552

Matthew De Courcy-Ireland

Publication date: 28 March 2024

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.12411

zbMATH Keywords

Euler characteristicplanar graphscubic surfacesgraph embeddingsexpander graphstotient functionMarkoff triples

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Cubic and quartic Diophantine equations (11D25) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Dynamical systems over finite ground fields (37P25)

Cites Work

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• \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
• The Markoff group of transformations in prime and composite moduli. With an appendix by Dan Carmon.
• Kesten-McKay law for the Markoff surface mod \(p\)
• Fractal geometry of the complement of Lagrange spectrum in Markov spectrum
• The cycle structure of a Markoff automorphism over finite fields
• Markov spectra for modular billiards
• Über eine Eigenschaft der ebenen Komplexe
• Markov's Theorem and 100 Years of the Uniqueness Conjecture
• A Separator Theorem for Planar Graphs
• Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
• A Proof of the Divergence of σ1/p
• Experiments with the Markoff Surface
• Gap sets for the spectra of cubic graphs
• Nonabelian level structures, Nielsen equivalence, and Markoff triples

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