A. K. Kel'mans, “Asymptotic formulas for the probability of $k$-connectedness of random graphs”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 253–265; Theory Probab. Appl., 17:2 (1973), 243

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Teoriya Veroyatnostei i ee Primeneniya, 1972, Volume 17, Issue 2, Pages 253–265 (Mi tvp2526)

This article is cited in 19 scientific papers (total in 19 papers)

Asymptotic formulas for the probability of

k

$k$ -connectedness of random graphs

A. K. Kel'mans

Moscow

Full-text PDF (643 kB) Citations (19)

Abstract: For graphs with vertices of sufficiently large, in a certain sense, degrees, asymptotical formulas are derived for the probability of

k

$k$ -connectedness of vertex subsets provided the edges of graphs are removed independently with given probabilities.

Received: 22.07.1970

English version:
Theory of Probability and its Applications, 1973, Volume 17, Issue 2, Pages 243–254
DOI: https://doi.org/10.1137/1117029

Bibliographic databases:

Language: Russian

Citation: A. K. Kel'mans, “Asymptotic formulas for the probability of

k

$k$ -connectedness of random graphs”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 253–265; Theory Probab. Appl., 17:2 (1973), 243–254

Citation in format AMSBIB

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\by A.~K.~Kel'mans

\paper Asymptotic formulas for the probability of $k$-connectedness of random graphs

\jour Teor. Veroyatnost. i Primenen.

\yr 1972

\vol 17

\issue 2

\pages 253--265

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=298723}

\zmath{https://zbmath.org/?q=an:0253.05136}

\transl

\jour Theory Probab. Appl.

\yr 1973

\vol 17

\issue 2

\pages 243--254

\crossref{https://doi.org/10.1137/1117029}

Linking options:

https://www.mathnet.ru/eng/tvp2526

https://www.mathnet.ru/eng/tvp/v17/i2/p253

This publication is cited in the following 19 articles:

Driss Bennis, Raja L'hamri, Khalid Ouarghi, “Zero-divisor super- $\lambda$ graphs”, São Paulo J. Math. Sci., 17:2 (2023), 789
Shuang Zhao, Yingzhi Tian, Jixiang Meng, “Degree Sequence Conditions for Maximally Edge-Connected and Super Edge-Connected Hypergraphs”, Graphs and Combinatorics, 36:4 (2020), 1065
Shangwei Lin, Jianfeng Pei, Chunfang Li, “Super Edge-Connected Linear Hypergraphs”, Parallel Process. Lett., 30:03 (2020), 2040003
Zhi-Hong He, Mei Lu, “Super-Edge-Connectivity and Zeroth-Order Randić Index”, J. Oper. Res. Soc. China, 7:4 (2019), 615
Zhi-hong He, Mei Lu, “Super Edge-connectivity and Zeroth-order General Randić Index for -1 ≤ α < 0”, Acta Math. Appl. Sin. Engl. Ser., 34:4 (2018), 659
Xing Chen, Juan Liu, Dongyang Xie, Jixiang Meng, “Edge connectivity and super edge-connectivity of jump graphs”, Journal of Information and Optimization Sciences, 37:2 (2016), 233
Yingzhi Tian, Jixiang Meng, Hongjian Lai, Zhao Zhang, “On the existence of super edge-connected graphs with prescribed degrees”, Discrete Mathematics, 328 (2014), 36
P. Dankelmann, J. D. Key, B. G. Rodrigues, “Codes from incidence matrices of graphs”, Des. Codes Cryptogr., 68:1-3 (2013), 373
Litao Guo, Ruifang Liu, Xiaofeng Guo, “Super λ3-optimality of regular graphs”, Applied Mathematics Letters, 25:2 (2012), 128
Yingzhi Tian, Litao Guo, Jixiang Meng, Chengfu Qin, “Inverse degree and super edge-connectivity”, International Journal of Computer Mathematics, 89:6 (2012), 752
Jun Yuan, Aixia Liu, Shiying Wang, “Sufficient conditions for bipartite graphs to be super-k-restricted edge connected”, Discrete Mathematics, 309:9 (2009), 2886
Angelika Hellwig, Lutz Volkmann, “Maximally edge-connected and vertex-connected graphs and digraphs: A survey”, Discrete Mathematics, 308:15 (2008), 3265
Angelika Hellwig, Lutz Volkmann, “Sufficient conditions for graphs to be λ′‐optimal, super‐edge‐connected, and maximally edge‐connected”, Journal of Graph Theory, 48:3 (2005), 228
Angelika Hellwig, Lutz Volkmann, “Neighborhood and degree conditions for super-edge-connected bipartite digraphs”, Results. Math., 45:1-2 (2004), 45
Brian D. Jones, Boris G. Pittel, Joseph S. Verducci, “Tree and forest weights and their application to nonuniform random graphs”, Ann. Appl. Probab., 9:1 (1999)
A. D. Korshunov, “The main properties of random graphs with a large number of vertices and edges”, Russian Math. Surveys, 40:1 (1985), 121–198
Béla Bollobás, Andrew Thomason, North-Holland Mathematics Studies, 118, Random Graphs '83, Based on lectures presented at the 1st Poznań Seminar on Random Graphs, 1985, 47
Yu. D. Burtin, “On extreme metric parameters of a random graph, I”, Theory Probab. Appl., 19:4 (1975), 710–725
Linda Lesniak, “Results on the edge-connectivity of graphs”, Discrete Mathematics, 8:4 (1974), 351

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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