4 - On random graphs from a minor-closed class
Published online by Cambridge University Press: 05 May 2016
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Random Graphs, Geometry and Asymptotic Structure , pp. 102 - 120Publisher: Cambridge University PressPrint publication year: 2016
References
[3] and , Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc., 22 (2009), 309–329.Google Scholar
[4] , , and , The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.Google Scholar
[5] , , , , and , Asymptotic enumeration and limit laws for graphs of fixed genus, J. Combin. Theory A, 118 (2011), 748–777.Google Scholar
[6] and , Asymptotic enumeration of labelled graphs with a given genus, Electron. J. Combin., 18 (2011), #P13.Google Scholar
[10] , The minimum Hadwiger number for graphs of a given mean degree of vertices (in Russian), Metody Diskret. Anal., 38 (1982), 37–58.Google Scholar
[11] , An extremal function for contractions of graphs, Math. Proc. Cambridge Philos. Soc., 95 (1984), 261–265.Google Scholar
[12] , , , and , Proper minor-closed families are small, J. Combin. Theory B, 96 (2006), 754–757.Google Scholar
[13] and , Small graph classes and bounded expansion, J. Combin. Theory B, 100 (2010), 171–175.Google Scholar
[15] , Some remarks on the theory of trees, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 4 (1959), 73–85.Google Scholar
[18] , On the enumeration of trees, Combinatorial Structures and Their Applications, , , , and (Eds), Gordon and Breach, New York, 1970, 355–360.Google Scholar
[19] , , and , Random graphs from planar and other addable classes, Topics in Discrete Mathematics, , , , , , and (Eds), Algorithms and Combinatorics 26. Springer, 2006, 231–246.Google Scholar
[20] , , and , Connectivity of addable graph classes, J. Combin. Theory B, 98 (2008), 577–584.Google Scholar
[21] , , and , Connectivity of random addable graphs, Proc. ICDM 2008, 13 (2010), 127–134.Google Scholar
[22] , , and , Connectivity for bridge-addable monotone graph classes, Combin. Prob. Comput., 21 (2012), 803–815.Google Scholar
[23] and , On the connectivity of random graphs from addable classes, J. Combin. Theory B, 103 (2013), 306–312.Google Scholar
[24] and , Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture, arXiv:1238952 [math.CO] April 2015.CrossRefGoogle Scholar
[26] , Connectivity for random graphs from a weighted bridge-addable class, Electronic J. Combin., 19(4) (2012), P53.Google Scholar
[27] , , and , Growth constants of minor-closed classes of graphs, J. Combin. Theory B, 100 (2010), 468–484.Google Scholar
[28] , Random graphs from a minor-closed class, Combin. Prob. Comput., 18 (2009), 583–599.Google Scholar
[29] and , A Course in Combinatorics, 2nd edn., Cambridge University Press, Cambridge, 2001.Google Scholar
[31] , Hadwiger's Conjecture, manuscript, 2015.Google Scholar
[32] and , Counting planar graphs and related families of graphs, in Surveys in Combinatorics 2009, 169–329, Cambridge University Press, Cambridge, 2009.Google Scholar
[33] , , , , and , Planar graphs, via well-orderly maps and trees, Graphs Combin., 22 (2) (2006), 185–202.Google Scholar
[34] , , and , Coefficients of functional compositions often grow smoothly, Electron. J. Combin., 15 (2008), #R21.Google Scholar
[35] and , Asymptotic properties of some minor-closed classes of graphs, Combin. Prob. Comput., 23 (5) (2014), 749–795.Google Scholar
[36] , , , and , Enumeration and limit laws for series-parallel graphs, European Journal of Combinatorics, 28 (2007), 2091–2105.Google Scholar
[37] , Connectivity and related properties for graph classes, DPhil thesis, Oxford University, 2013.Google Scholar
[38] , Random graphs from a weighted minor-closed class, Electronic J. Combin., 20 (2) (2013), P52, 39 pages.Google Scholar
[39] and , Random unlabelled graphs containing few disjoint cycles, Random Structures Algorithms, 38 (2011), 174–204.Google Scholar
[40] and , Random graphs with few disjoint cycles, Combin. Prob. Comput., 20 (2011), 763–775.Google Scholar
[41] and , Random graphs containing few disjoint excluded minors, Random Structures Algorithms, 44 (2) (2014), 240–268.Google Scholar
[42] , On graphs with few disjoint t-star minors, European J. Combin., 32 (2011), 1394–1406.Google Scholar
[43] , On graphs containing few disjoint excluded minors, asymptotic number and structure of graphs containing few disjoint minors K4, arXiv: 1504.08107v1 [math.CO] 2015.Google Scholar