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Number of Eulerian orientations for Benjamini--Schramm convergent graph sequences (2409.18012v1)
Published 26 Sep 2024 in math.CO
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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