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Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2018

Cubic graphs and related triangulations on orientable surfaces

Résumé

Let $\mathbb{S}_g$ be the orientable surface of genus $g$. We show that the number of vertex-labelled cubic multigraphs embeddable on $\mathbb{S}_g$ with $2n$ vertices is asymptotically $c_g n^{5(g-1)/2-1}\gamma^{2n}(2n)!$, where $\gamma$ is an algebraic constant and $c_g$ is a constant depending only on the genus $g$. We also derive an analogous result for simple cubic graphs and weighted cubic multigraphs. Additionally we prove that a typical cubic multigraph embeddable on $\mathbb{S}_g$, $g\ge 1$, has exactly one non-planar component.

Dates et versions

hal-02338112 , version 1 (29-10-2019)

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Wenjie Fang, Mihyun Kang, Michael Mosshammer, Philipp Sprüssel. Cubic graphs and related triangulations on orientable surfaces. The Electronic Journal of Combinatorics, 2018. ⟨hal-02338112⟩
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