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2 - Random graphs from restricted classes

Published online by Cambridge University Press:  05 May 2016

Michael Krivelevich
Affiliation:
Tel-Aviv University
Konstantinos Panagiotou
Affiliation:
Universität Munchen
Mathew Penrose
Affiliation:
University of Bath
Colin McDiarmid
Affiliation:
University of Oxford
Nikolaos Fountoulakis
Affiliation:
University of Birmingham
Dan Hefetz
Affiliation:
University of Birmingham
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Publisher: Cambridge University Press
Print publication year: 2016

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References

[1] Bollobás, Béla, Random Graphs, 2nd edn, Cambridge University Press, Cambridge, 2001.CrossRefGoogle Scholar
[2] Janson, Svante, Luczak, Tomasz, and Ruciński, Andrzej, Random Graphs, Wiley, New York, NY, 2000.CrossRefGoogle Scholar
[3] Flajolet, Philippe and Sedgewick, Robert, Analytic Combinatorics. Cambridge University Press, Cambridge, 2009.CrossRefGoogle Scholar
[4] Duchon, Philippe, Flajolet, Philippe, Louchard, Guy, and Schaeffer, Gilles, Boltzmann samplers for the random generation of combinatorial structures, Comb. Probab. Comput., 13(4–5) (2004), 577–625.Google Scholar
[5] Flajolet, Philippe, Fusy, Éric, and Pivoteau, Carine, Boltzmann sampling of unlabelled structures. Pages 201–211 of: Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithmics and Combinatorics. SIAM, Philadelphia, PA, 2007.Google Scholar
[6] Bodirsky, Manuel, Fusy, Éric, Kang, Mihyun, and Vigerske, Stefan, Boltzmann samplers, Pólya theory, and cycle pointing, SIAM J. Comput., 40(3) (2011), 721–769.CrossRefGoogle Scholar
[7] Alon, Noga and Spencer, Joel H., The Probabilistic Method. With an Appendix on the Life and Work of Paul Erdõs, 3rd edn, John Wiley & Sons, Hoboken, NJ, 2008.Google Scholar
[8] Davis, Burgess and McDonald, David, An elementary proof of the local central limit theorem, J. Theor. Probab., 8(3) (1995), 693–701.CrossRefGoogle Scholar
[9] Drmota, Michael, Random Trees. An Interplay between Combinatorics and Probability, Springer, Wien, 2009.Google Scholar
[10] Janson, Svante, Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation, Probab. Surv., 9 (2012), 103–252.CrossRefGoogle Scholar
[11] Takacs, Lajos, A generalization of the ballot problem and its application in the theory of queues, J. Am. Stat. Assoc., 57 (1962), 327–337.Google Scholar
[12] Diestel, Reinhard, Graph Theory. Graduate Texts in Mathematics, vol. 173, Springer, 2010.Google Scholar
[13] Giménez, Omer and Noy, Marc, Asymptotic enumeration and limit laws of planar graphs, J. Am. Math. Soc., 22(2) (2009), 309–329.Google Scholar
[14] Panagiotou, Konstantinos and Steger, Angelika, Maximal biconnected subgraphs of random planar graphs, ACM Trans. Algorithms, 6(2) (2010), 21.CrossRefGoogle Scholar
[15] Fountoulakis, Nikolaos and Panagiotou, Konstantinos, 3-connected cores in random planar graphs, Comb. Probab. Comput., 20(3) (2011), 381–412.CrossRefGoogle Scholar
[16] Giménez, Omer, Noy, Marc, and Rué, Juanjo, Graph classes with given 3-connected components: asymptotic enumeration and random graphs, Random Struct. Algorithms, 42(4) (2013), 438–479.CrossRefGoogle Scholar
[17] Drmota, Michael, Fusy, Éric, Kang, Mihyun, Kraus, Veronika, and Rué, Juanjo, Asymptotic study of subcritical graph classes, SIAM J. Discrete Math., 25(4) (2011), 1615–1651.CrossRefGoogle Scholar
[18] Bernasconi, Nicla, Panagiotou, Konstantinos, and Steger, Angelika, The degree sequence of random graphs from subcritical classes, Comb. Probab. Comput., 18(5) (2009), 647–681.CrossRefGoogle Scholar
[19] Drmota, Michael, Giménez, Omer, and Noy, Marc, Degree distribution in random planar graphs, J. Comb. Theory, Ser. A, 118(7) (2011), 2102–2130.CrossRefGoogle Scholar
[20] Panagiotou, Konstantinos, Stufler, Benedikt, and Weller, Kerstin, Scaling limits of random graphs from subcritical classes, Ann. of Prob. Accepted for publication.Google Scholar
[21] Joyal, André, Une théorie combinatoire des séries formelles, Adv. in Math., 42(1) (1981), 1–82.CrossRefGoogle Scholar
[22] Bergeron, F., G., Labelle, and P., Leroux, Combinatorial Species and Tree-like Structures. Encyclopedia of Mathematics and Its Applications, vol. 67. Cambridge University Press, Cambridge, 1998. Translated from the 1994 French original by Margaret Readdy, with a foreword by Gian-Carlo Rota.Google Scholar
[23] Fusy, Éric, Uniform random sampling of planar graphs in linear time, Random Struct. Algorithms, 35(4) (2009), 464–522.CrossRefGoogle Scholar
[24] Harary, Frank and Palmer, Edgar M., Graphical Enumeration. Academic Press, New York-London, 1973.Google Scholar
[25] Gerke, Stefanie, Giménez, Omer, Noy, Marc, and Weißl, Andreas, The number of graphs not containing K3,3 as a minor, Electron. J. Comb., 15(1) (2008), research paper r114, 20.Google Scholar
[26] Tutte, William Thomas, Connectivity in Graphs. University of Toronto Press, Toronto, (1996).Google Scholar

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