Previous article Next article Asymptotic Formulas for the Probability of k-Connectedness of Random GraphsA. K. Kel’mansA. K. Kel’manshttps://doi.org/10.1137/1117029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. A. Zykov, Theory of Finite Graphs, “Nauka”, Novosibirsk, 1969, (In Russian) 0213.25801 Google Scholar[2] E. N. Gilbert, Random graphs, Ann. Math. Statist., 30 (1959), 1141–1144 MR0108839 0168.40801 CrossrefGoogle Scholar[3] P. Erdo˝s and , A. Rényi, On random graphs. I, Publ. Math. Debrecen, 6 (1959), 290–297 MR0120167 0092.15705 Google Scholar[4] P. Erdös and , A. Renyi, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 17–61 0103.16301 Google Scholar[5] P. Erdo˝s and , A. Rényi, On the strength of connectedness of a random graph, Acta Math. Acad. Sci. Hungar., 12 (1961), 261–267 MR0130187 0103.16302 CrossrefGoogle Scholar[6] N. Palásti, On the connectedness of bichromatic random graphs, Publ. Math. Inst. Hung. Acad. Sci., 8 (1963), 431–441 0134.43503 Google Scholar[7] A. K. Kel'mans, Some problems of the analysis of reliability of nets, Avtomatika i Telemechanika, 26 (1965), 567–574, (In Russian.) 0228.94025 Google Scholar[8] A. K. Kel'mans, On connectedness of probability nets, Avtomatika i Telemechanika, 28 (1967), 98–116 Google Scholar[9] A. K. Kelmans, Questions of analysis and synthesis of probabilistic networks, Proceedings of the First All-Union Symposium on Statistical Problems in Engineering Cybernetics (Moscow, 1967): Adaptive systems, Large systems (Russian), Izdat. “Nauka”, Moscow, 1971, 264–273 MR0386880 Google Scholar[10] V. E. Stepanov, Combinatorial algebra and random graphs, Theory Prob. Applications, 14 (1969), 373–399 10.1137/1114052 0239.05124 LinkGoogle Scholar[11] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461 MR0088081 0077.12201 Google Scholar[12] I. N. Sanov, On the probability of large deviations of random magnitudes, Mat. Sb. N. S., 42 (84) (1957), 11–44, (In Russian.) MR0088087 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Zero-divisor super-$$\lambda$$ graphs23 June 2022 | São Paulo Journal of Mathematical Sciences, Vol. 1 Cross Ref Super Edge-Connected Linear Hypergraphs12 October 2020 | Parallel Processing Letters, Vol. 30, No. 03 Cross Ref Degree Sequence Conditions for Maximally Edge-Connected and Super Edge-Connected Hypergraphs11 April 2020 | Graphs and Combinatorics, Vol. 36, No. 4 Cross Ref Super-Edge-Connectivity and Zeroth-Order Randić Index3 October 2018 | Journal of the Operations Research Society of China, Vol. 7, No. 4 Cross Ref Super Edge-connectivity and Zeroth-order General Randić Index for −1 ≤ α < 04 October 2018 | Acta Mathematicae Applicatae Sinica, English Series, Vol. 34, No. 4 Cross Ref Edge connectivity and super edge-connectivity of jump graphs18 April 2016 | Journal of Information and Optimization Sciences, Vol. 37, No. 2 Cross Ref On the existence of super edge-connected graphs with prescribed degreesDiscrete Mathematics, Vol. 328 Cross Ref Codes from incidence matrices of graphs3 January 2012 | Designs, Codes and Cryptography, Vol. 68, No. 1-3 Cross Ref Inverse degree and super edge-connectivityInternational Journal of Computer Mathematics, Vol. 89, No. 6 Cross Ref Super λ3 -optimality of regular graphsApplied Mathematics Letters, Vol. 25, No. 2 Cross Ref Sufficient conditions for bipartite graphs to be super- k -restricted edge connectedDiscrete Mathematics, Vol. 309, No. 9 Cross Ref Maximally edge-connected and vertex-connected graphs and digraphs: A surveyDiscrete Mathematics, Vol. 308, No. 15 Cross Ref Sufficient conditions for graphs to be ??-optimal, super-edge-connected, and maximally edge-connected1 January 2005 | Journal of Graph Theory, Vol. 48, No. 3 Cross Ref Neighborhood and degree conditions for super-edge-connected bipartite digraphs24 April 2013 | Results in Mathematics, Vol. 45, No. 1-2 Cross Ref Tree and forest weights and their application to nonuniform random graphsThe Annals of Applied Probability, Vol. 9, No. 1 Cross Ref Random Graphs of Small Order Cross Ref On Extreme Metric Parameters of a Random Graph. I. Asymptotic EstimatesYu. D. Burtin28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 4AbstractPDF (1056 KB)Results on the edge-connectivity of graphsDiscrete Mathematics, Vol. 8, No. 4 Cross Ref Volume 17, Issue 2| 1973Theory of Probability & Its Applications History Submitted:22 July 1970Published online:17 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117029Article page range:pp. 243-254ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics