Geodesic
Asymptotical enumeration of labeled series-parallel tetracyclic graphs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 31-35

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A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. We find an asymptotics for the number of labeled connected series-parallel tetracyclic graphs with a large number of vertices. We prove that under a uniform probability distribution, the probability of the fact that a labeled connected tetracyclic graph is a series-parallel graph is asymptotically equal to $141/221$.
Keywords: enumeration, labeled graph, series-parallel graph, asymptotics, probability. 
@article{INTO_2020_187_a3,
     author = {V. A. Voblyi},
     title = {Asymptotical enumeration of labeled series-parallel tetracyclic graphs},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {31--35},
     publisher = {mathdoc},
     volume = {187},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_187_a3/}
}
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V. A. Voblyi. Asymptotical enumeration of labeled series-parallel tetracyclic graphs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 31-35. http://geodesic.mathdoc.fr/item/INTO_2020_187_a3/