Generating outerplanar graphs uniformly at random

Combinatorics Probability and Computing

Volumn 15, Issue 3, 2006, Pages 333-343

  Bodirsky, Manuel ^a   Kang, Mihyun ^a,b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b European Graduate Program Combinatorics Geometry and Computation   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BLOCK STRUCTURE; COUNTING TECHNIQUE; OUTERPLANAR GRAPHS; POLYNOMIAL TIME;

ALGORITHMS; PROBABILITY; RANDOM PROCESSES; RECURSIVE FUNCTIONS;

GRAPH THEORY;

EID: 33645662954     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548305007303     Document Type: Article

References (30)

1. Alonso, L., Remy, J. and Schott, R. (1997) A linear-time algorithm for the generation of trees. Algorithmica 17 162-182.
2. Atallah, M. J. and Manning, J. (1992) Fast detection and display of symmetry in outerplanar graphs. Discrete Appl. Math. 39 13-35.
3. Banderier, C., Flajolet, P., Schaeffer, G. and Soria, M. (2001) Random maps, coalescing saddles, singularity analysis, and Airy phenomena. Random Struct. Alg. 19 194-246.
4. Bender, A., Gao, Z. and Wormald, N. (2002) The number of labeled 2-connected planar graphs. Electron. J. Combin 9 #43.
5. Biedl, T. (2002) Drawing outer-planar graphs in o(n log n) area. In 10th Annual Conference on Graph Drawing.
6. Bodlaender, H. L. and Fomin, F. V. (2001) Approximation of pathwidth of outerplanar graphs. In Proc. 27th International Workshop on Graph-Theoretic Concepts in Computer Science, Vol. 2204 of Lecture Notes in Computer Science, pp. 166-176.
7. Bürgisser, P., Clausen, M. and Shokrollahi, M. (1997) Algebraic Complexity Theory, Vol. 315 of Grundlehren der Mathematischen Wissenschaften, Springer.
8. Chartrand, G. and Harary, F. (1967) Planar permutation graphs. Ann. Inst. H. Poincaré, Sec. B3, pp. 433-438.
9. Denise, A., Vasconcellos, M. and Welsh, D. (1996) The random planar graph. Congressus Numerantium 113 61-79.
10. Denise, A. and Zimmermann, P. (1999) Uniform random generation of decomposable structures using floating-point arithmetic. Theoret. Comput. Sci. 218 233-248.
11. Devroye, L., Flajolet, P., Hurtado, F., Noy, M. and Steiger, W. (1999) Properties of random triangulations and trees. Discrete Comput. Geom. 22 105-117.
12. Diestel, R. (1997) Graph Theory, Springer, New York.
13. Epstein, P. and Sack, J.-R. (1994) Generating triangulations at random. ACM Trans. Model. Comput. Simul. 4 267-278.
14. Gerke, S. and McDiarmid, C. On the number of edges in random planar graphs. Submitted.
15. Govindran, R., Langston, M. and Yan, X. (1998) Approximating the pathwidth of outerplanar graphs. Inform. Process. Lett. 68 17-23.
16. Gurevich, Y. (1991) Average case completeness. J. Comput. System Sci. 42 346-398.
17. Harary, R. and Palmer, E. M. (1973) Graphical Enumeration, Academic Press, New York and London.
18. 2 algorithm for determining isomorphism of planar graphs. Inform. Process. Lett. 1(1) 32-34.
19. Lenhart, W. and Liotta, G. (1997) Proximity drawings of outerplanar graphs. In Graph Drawing; Proc. GD '96 (S. North, ed.), Vol. 1190 of Lecture Notes in Computer Science, pp. 286-302.
20. Levin, L. (1986) Average case complete problems. SIAM J. Comput. 15 285-286.
21. Leydold, J. and Stadler, P. F. (1998) Minimal cycle bases of outerplanar graphs. Electron J. Combin. 5 #16.
22. McShine, L. and Tetali, P. (1999) On the mixing time of the triangulation walk and other Catalan structures. In Vol. 43 of DIMACS Series in Discrete Math. Theor. Comput. Sci., pp. 147-159.
23. Mitchell, S. L. (1979) Linear algorithms to recognize outerplanar and maximal outerplanar graphs. Inform. Process. Lett. 9 229-232.
24. Molloy, M., Reed, B. and Steiger, W. (1999) On the mixing rate of the triangulation walk. In Vol. 43 of DIMACS Series in Discrete Math. Theor. Comput. Sci., pp. 179-190.
25. Nijenhuis, A. and Wilf, H. (1979) Combinatorial Algorithms, Academic Press.
26. Okamura, H. and Seymour, P. (1981) Multicommodity flows in planar graphs. J. Combin. Theory Ser. B 31 75-81.
27. Osthus, D., Prömel, H. J. and Taraz, A. On random planar graphs, the number of planar graphs and their triangulations. J. Combin. Theory Ser. B, to appear.
28. Schaeffer, G. (1999) Random sampling of large planar maps and convex polyhedra. In Proc. 31st Annual ACM Symposium on Theory of Computing (STOC'99, Atlanta, Georgia, May 1999), ACM Press, pp. 760-769.
29. Schröder, E. (1870) Vier combinatorische Probleme. Z. Math. Physik 15 361-376.
30. Sloane, N. J. A. Sequence A001003: The on-line encyclopedia of integer sequences, http://www.research.att.com/~njas/sequences/.