Geodesic
Cubic graphs and related triangulations on orientable surfaces
Wenjie Fang1 ; Mihyun Kang1 ; Michael Moßhammer1 ; Philipp Sprüssel1
1Graz University of Technology
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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Let $\mathbb{S}_g$ be the orientable surface of genus $g$ for a fixed non-negative integer $g$. We show that the number of vertex-labelled cubic multigraphs embeddable on $\mathbb{S}_g$ with $2n$ vertices is asymptotically $c_g n^{5/2(g-1)-1}\gamma^{2n}(2n)!$, 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, for $g\ge1$, we prove that a typical cubic multigraph embeddable on $\mathbb{S}_g$ has exactly one non-planar component.
DOI : 10.37236/5989
Classification : 05A16, 05C10, 05C30
Mots-clés : cubic graphs, graphs on surfaces, triangulations, asymptotic enumeration, analytic combinatorics

Wenjie Fang  1   ; Mihyun Kang  1   ; Michael Moßhammer  1   ; Philipp Sprüssel  1

1 Graz University of Technology 
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     title = {Cubic graphs and related triangulations on orientable surfaces},
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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, Tome 25 (2018) no. 1. doi: 10.37236/5989

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