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. 
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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/

[1] Voblyi V. A., “O perechislenii pomechennykh svyaznykh grafov s zadannymi chislami vershin i reber”, Diskr. anal. issl. oper., 23:2 (2016), 5–20 | Zbl

[2] Voblyi V. A., “Chislo pomechennykh vneshneplanarnykh grafov $k$-tsiklicheskikh grafov”, Mat. zametki., 103:5 (2018), 657–666 | MR | Zbl

[3] Voblyi V. A., “Vtoroe sootnoshenie Riddela i sledstviya iz nego”, Diskr. anal. issl. oper., 26:1 (2019), 20–32 | Zbl

[4] Voblyi V. A., “Perechislenie pomechennykh posledovatelno-parallelnykh tritsiklicheskikh grafov”, Itogi nauki tekhn. Ser. Sovr. mat. prilozh. Temat. obzory., 177 (2020), 132–136

[5] Voblyi V. A., “Chislo pomechennykh posledovatelno-parallelnykh tetratsiklicheskikh blokov”, Prikl. diskr. mat., 2020, no. 47, 57–61 | Zbl

[6] Voblyi V. A., Meleshko A. M., “O chisle pomechennykh posledovatelno-parallelnykh tritsiklicheskikh blokov”, Mat. XV Mezhdunar. konf. «Algebra, teoriya chisel i diskretnaya geometriya. Sovremennye problemy i prilozheniya» (Tula, 28-31 maya 2018 g.), TPGU, Tula, 168–170

[7] Gulden Ya., Dzhekson D., Perechislitelnaya kombinatorika, Nauka, M., 1990 | MR

[8] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982 | MR

[9] Bodirsky M., Gimenez O., Kang M., Noy M., “Enumeration and limit laws of series-parallel graphs”, Eur. J. Combin., 28:8 (2007), 2091–2105 | DOI | MR | Zbl

[10] McDiarmid C., Scott A., “A random graphs from a block stable class”, Eur. J. Combin., 58 (2016), 96–106 | DOI | MR | Zbl

[11] Radhavan S., “Low-connectivity network design on series-parallel graphs”, Networks., 43:3 (2004), 163–176 | DOI | MR

[12] Wright E. M., “The number of connected sparsely edged graphs, II”, J. Graph Theory., 2:4 (1978), 299–305 | DOI | MR | Zbl

[13] Wright E. M., “The number of connected sparsely edged graphs, III”, J. Graph Theory., 4:4 (1980), 393–407 | DOI | MR | Zbl