Random sampling of large planar maps and convex polyhedra

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	1	M. E. Agishtein and A. A. Migdal. Recursive sampling of planar graphs and fractal properties of a two-dimensional quantum gravity. Internat. J. Modern Phys. 6', 1(1):165- 179, 1990.
	2	L. Alonso, J. L. R~my, and 1~. Schott. A linear-time algorithm for the generation of trees. Algorithrnica, 17(2):162- 182, 1997.
	3	Edward A. Bender , E. Rodney Canfield , Zhicheng Gao , L. Bruce Ricmond, Submap Density and Asymmetry Results for Two Parameter Map Families, Combinatorics, Probability and Computing, v.6 n.1, p.17-25, March 1997 [doi>10.1017/S0963548396002799]
	4	Edward A. Bender , L. Bruce Richmond , Nicholas C. Wormald, Largest 4-connected components of 3-connected planar triangulations, Random Structures & Algorithms, v.7 n.4, p.273-285, Dec. 1995 [doi>10.1002/rsa.3240070402]
	5	E. A. Bender and N. C. Wormatd. The number of rooted convex polyhedra. Canad. Math. Bull., 31(1):99-102, 1988.
	6	M. Bousquet-M~lou and G. Schaeffer. Enumeration of planar constellations. Research Report 1209-98, LaBRI, Universit~ Bordeaux I, July 1998. 21 pages. To appear in Adv. in Applied Math.
	7	Richie Chih-Nan Chuang , Ashim Garg , Xin He , Ming-Yang Kao , Hsueh-I Lu, Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses, Proceedings of the 25th International Colloquium on Automata, Languages and Programming, p.118-129, July 13-17, 1998
	8	G. M. Cicuta, L. Motinari, E. Montaldi, and S. Stramaglia. A matrix model for random surfaces with dynamical holes. J. Phys. A, 29(14):3769-3785, 1996.
	9	A. Denise. Generation of random planar maps. In Graph Drawing'93, Paris, 1993.
	10	A. Denise, M. Vasconcellos, and D. J. A. Welsh. The random planar graph. Congr. Numer., 113:61-79, 1996. Festschrift for C. St. J. A. Nash-Williams.
	11	Alain Denise , Paul Zimmermann, Uniform random generation of decomposable structures using floating-point arithmetic, Theoretical Computer Science, v.218 n.2, p.233-248, May 6, 1999 [doi>10.1016/S0304-3975(98)00323-5]
	12	P. Flajolet, Z. Ggo, A. Odlyzko, and B. Richmond. The distribution of heights of binary trees and other simple trees. Combin. Probab. Comput., 2(2):145-156, 1993.
	13	Philippe Flajolet , Paul Zimmerman , Bernard Van Cutsem, A calculus for the random generation of labelled combinatorial structures, Theoretical Computer Science, v.132 n.1-2, p.1-35, Sept. 26, 1994 [doi>10.1016/0304-3975(94)90226-7]
	14	J. E. Hopcroft and R. E. Tarjan. Dividing a graph into triconnected components. SIAM J. Comput., 2:135-158, 1973.
	15	Benjamin Jacquard , Gilles Schaeffer, A bijective census of nonseparable planar maps, Journal of Combinatorial Theory Series A, v.83 n.1, p.1-20, July 1998 [doi>10.1006/jcta.1997.2852]
	16	Brendan D. McKay, Isomorph-free exhaustive generation, Journal of Algorithms, v.26 n.2, p.306-324, feb. 1998 [doi>10.1006/jagm.1997.0898]
	17	R. C. Mullin and P. J. Schellenberg. The enumeration of cnets via quadrangulations. J. Combinatorial Theory, 4:259- 276, 1968.
	18	J. I. Munro , V. Raman, Succinct representation of balanced parentheses, static trees and planar graphs, Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS '97), p.118, October 19-22, 1997
	19	Pigale, An Automatic Graph Drawing Project. Atelier de taxiplanie, CAMS, l~cole des Hautes t~tudes en Sciences Sociales, Paris. Part of ALCOM-IT, ESPRIT LTR Projet 20244.
	20	L. B. Richmond , N. C. Wormald, Almost all maps are asymmetric, Journal of Combinatorial Theory Series B, v.63 n.1, p.1-7, Jan. 1995 [doi>10.1006/jctb.1995.1001]
	21	G. Schaeffer. Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees. Electron. J. Combin., 4(1):Research Paper 20, 14 pp. (electronic), 1997.
	22	G. Schaeffer. Conjugaison d'arbres et cartes combinatoires al4atoires. PhD thesis, Universit6 Bordeaux I, 1998.
	23	W. T. Tutte. A census of planar maps. Canad. J. Math., 15:249-271, 1963.
	24	W. T. Tutte. Duality and trinity. In Infinite and finite sets, Vot. III, pages 1459-1472. Colloq. Math. Soc. Janos Bolyai, Vol. 10, Amsterdam, 1975. North-Holland.
	25	David Bruce Wilson, Determinant algorithms for random planar structures, Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms, p.258-267, January 05-07, 1997, New Orleans, Louisiana, United States
	26	D. B. Wilson. Annotated bibliography of perfectly random sampling with Markov chains. In Microsurveys in Discrete Probability, volume 41 of DIMACS, pages 209-220, 1998. Updated at http://dimacs, rutgers, edu/'dbwilson/exact.

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