Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 223, Pages 138–147
DOI: https://doi.org/10.36535/0233-6723-2023-223-138-147 (Mi into1163) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On enumeration of labeled connected bridgeless graphs

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.36535/0233-6723-2023-223-138-147
Abstract: In this paper, we obtain explicit formulas and asymptotics for some classes of bridgeless labeled graphs: cacti, block graphs, block-cactus graphs, and series-parallel graphs. We prove that, under a uniform probability distribution, almost all graphs from the classes considered have bridges.
Keywords: enumeration, labeled graph, $k$-cyclic graph, block, bridge, bridgeless graph, Eulerian graph, series-parallel graph, asymptotics, random graph.
Document Type: Article
UDC: 519.175.3
MSC: 05C30
Language: Russian
Citation: V. A. Voblyi, “On enumeration of labeled connected bridgeless graphs”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 223, VINITI, Moscow, 2023, 138–147
Citation in format AMSBIB
\Bibitem{Vob23}
\by V.~A.~Voblyi
\paper On enumeration of labeled connected bridgeless graphs
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 223
\pages 138--147
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1163}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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