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arXiv · 2409.18012

Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences

Ferenc Bencs·Márton Borbényi·Péter Csikvári
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Abstract

For a graph $G$ let $\varepsilon(G)$ denote the number of Eulerian orientations, and $v(G)$ denote the number of vertices of $G$. We show that if $(G_n)_n$ is a sequence of Eulerian graphs that are convergent in Benjamini--Schramm sense, then $\lim\limits_{n\to \infty}\frac{1}{v(G_n)}\ln \varepsilon(G_n)$ is convergent.

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Ferenc Bencs, Márton Borbényi, Péter Csikvári. 2024-09-26. Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences. https://arxiv.org/abs/2409.18012

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