Random Plane Networks

Previous article Next article Random Plane NetworksE. N. GilbertE. N. Gilberthttps://doi.org/10.1137/0109045PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 T. L. Austin, , R. E. Fagen, , W. F. Penney and , John Riordan, The number of components in random linear graphs, Ann. Math. Statist, 30 (1959), 747–754 MR0115939 0088.11602 CrossrefISIGoogle Scholar2 S. R. Broadbent and , J. M. Hammersley, Percolation processes. I. Crystals and mazes, Proc. Cambridge Philos. Soc., 53 (1957), 629–641 MR0091567 0091.13901 CrossrefGoogle Scholar3 P. Erdo˝s and , A. Rényi, On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl., 5 (1960), 17–61 MR0125031 Google Scholar4 William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461 MR0088081 Google Scholar5 E. N. Gilbert, Random graphs, Ann. Math. Statist., 30 (1959), 1141–1144 MR0108839 0168.40801 CrossrefISIGoogle Scholar6 J. M. Hammersley, Percolation processes. II. The connective constant, Proc. Cambridge Philos. Soc., 53 (1957), 642–645 MR0091568 0091.13902 CrossrefGoogle Scholar7 J. M. Hammersley, Percolation processes: Lower bounds for the critical probability, Ann. Math. Statist., 28 (1957), 790–795 MR0101564 0091.13903 CrossrefISIGoogle Scholar8 J. M. Hammersley, Bornes supérieures de la probabilité critique dans un processus de filtrationLe calcul des probabilités et ses applications. Paris, 15-20 juillet 1958, Colloques Internationaux du Centre National de la Recherche Scientifique, LXXXVII, Centre National de la Recherche Scientifique, Paris, 1959, 17–37 MR0105751 0096.11502 Google Scholar9 T. E. Harris, A lower bound for the critical probability in a certain percolation process, Proc. Cambridge Philos. Soc., 56 (1960), 13–20 MR0115221 0122.36403 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On Treewidth and Related Parameters of Random Geometric GraphsDieter Mitsche and Guillem PerarnauSIAM Journal on Discrete Mathematics, Vol. 31, No. 2 | 22 June 2017AbstractPDF (619 KB)Mean Square Performance of Consensus-Based Distributed Estimation over Regular Geometric GraphsSIAM Journal on Control and Optimization, Vol. 50, No. 1 | 19 January 2012AbstractPDF (397 KB)Sharp Threshold for Hamiltonicity of Random Geometric GraphsSIAM Journal on Discrete Mathematics, Vol. 21, No. 1 | 26 January 2007AbstractPDF (148 KB)Percolation Processes and Related TopicsH. L. Frisch and J. M. HammersleyJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 4 | 13 July 2006AbstractPDF (2830 KB) Volume 9, Issue 4| 1961Journal of the Society for Industrial and Applied Mathematics489-699 History Submitted:14 December 1960Published online:10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0109045Article page range:pp. 533-543ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics