Alex Kontorovich

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math.CO2025

Effective resistance in planar graphs and continued fractions

Swee Hong Chan, Alex Kontorovich, Igor Pak

For a simple graph $G = (V, E)$ and edge $e \in E$ , the effective resistance is defined as a ratio $\frac{τ ( G / e )}{τ ( G )}$ , where $τ (G)$ denotes the number of spanning trees in $G$ . We r…

math.CO2024

Spanning trees and continued fractions

Swee Hong Chan, Alex Kontorovich, Igor Pak

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…