A better upper bound on the number of triangulations of a planar point set

Journal of Combinatorial Theory. Series A

Volumn 102, Issue 1, 2003, Pages 186-193

  Santos, Francisco ^a   Seidel, Raimund ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038706477     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-3165(03)00002-5     Document Type: Article

References (10)

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2. O. Aichholzer, F. Hurtado, M. Noy, On the number of triangulations every planar point set must have, in: Proceedings of the 13th Annual Canadian Conference on Computational Geometry CCCG 2001, Waterloo, Canada, 2001, pp. 13-16.
3. M. Ajtai, V. Chvátal, M. Newborn, E. Szemerédi, Crossing-free subgraphs, Ann. Discrete Math. 12 (1982) 9-12.
4. L.J. Billera, P. Filliman, B. Sturmfels, Constructions and complexity of secondary polytopes, Adv. Math. 83 (1990) 155-179.
5. M.O. Denny, C.A. Sohler, Encoding a triangulation as a permutation of its point set, Proceedings of the Ninth Canadian Conference on Computational Geometry, 1997, pp. 39-43.
6. N, Comput. Geom. 16 (2000) 211-221.
7. F. Hurtado, M. Noy, Counting triangulations of almost-convex polygons, Ars Combin. 45 (1997) 169-179.
8. V. Reiner, The generalized Baues problem, in: L.J. Billera, A. Björner, C. Greene, R.E. Simion, R.P. Stanley (Eds.), New Perspectives in Algebraic Combinatorics, Vol. 38, MSRI publications, Cambridge University Press, Cambridge, 1999, pp. 293-336.
9. R. Seidel, On the number of triangulations of planar point sets, Combinatorica 18 (1998) 297-299.
10. W.D. Smith, Studies in Computational geometry motivated by mesh generation, Ph.D. Thesis, Princeton University, 1989.