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

Cubic graphs and related triangulations on orientable surfaces

Résumé

Let Sg be the orientable surface of genus g. We show that the number of vertex-labelled cubic multigraphs embeddable on Sg with 2n vertices is asymptotically cgn5(g1)/21γ2n(2n)!, where γ is an algebraic constant and cg 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 Sg, g1, 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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