Under construction
Winter School in Guanajuato, 2010
The Erdös-Szekeres theorem and its relatives, references and
problems
1. The Erdös-Szekeres theorem
W. Morris, V. Soltan: The Erdös-Szekeres problem on points in convex
position - a survey,
Bulletin of the American Mathematical Society 37 (2000), 437-458.
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G. Tóth, P. Valtr:
The Erdös-Szekeres theorem, upper bounds and generalizations,
Discrete and Computational Geometry - Papers from the MSRI Special Program
(J. E. Goodman et al. eds.), MSRI Publications 52 Cambridge University Press, Cambridge (2005),
557-568.
pdf
Gy. Károlyi, P. Valtr:
Point configurations in d-space without large subsets in convex position,
U.S.-Hungarian Workshops on Discrete Geometry and Convexity (Budapest,
1999/Auburn, AL, 2000).
Discrete Comput. Geom. 30 (2003), 277-286.
pdf
2. Empty convex polygons
O. Aichholzer: [Empty] [colored] k-gons - Recent results on some
Erdös-Szekeres type problems. In: Proc. XIII Encuentros de Geometría
Computacional, pages 43-52, Zaragoza, Spain, 2009.
pdf
I. Bárány, Z. Füredi:
Empty simplices in Euclidean space,
Canad. Math. Bull. 30 (1987), 436-445.
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A. Dumitrescu:
Planar sets with few empty convex polygons,
Studia Sci. Math. Hungar. 36 (2000), 93-109.
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I. Bárány, P. Valtr:
Planar point sets with a small number of empty convex polygons,
Studia Sci. Math. Hungar. 41 (2004), 243-266.
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J. D. Horton,
Sets with no empty convex 7-gons,
Canad. Math. Bull. 26 (1983), 482-484.
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3. Empty convex polygons in colored point sets
O. Devillers, F. Hurtado, Gy. Károlyi, C. Seara:
Chromatic variants of the Erdős-Szekeres theorem on points in convex position,
Comput. Geom. 26 (2003), 193-208.
pdf
O. Aichholzer, R. Fabila-Monroy, D. Flores-Peńaloza, T. Hackl, C. Huemer,
J. Urrutia:
Empty monochromatic triangles,
Computational Geometry: Theory and Applications, 42 (2009),
934-938.
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J. Pach, G. Tóth:
Monochromatic empty triangles in two-colored point sets,
Geometry, Games, Graphs and Education: the Joe Malkevitch
Festschrift (S. Garfunkel, R. Nath, eds.), COMAP, Bedford, MA, 2008,
195-198.
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O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, and B. Vogtenhuber. Large
bichromatic point sets admit empty monochromatic 4-gons. SIAM Journal on
Discrete Mathematics (SIDMA), 23(9):2147-2155, 2010.
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4. The Erdős-Szekeres theorem for convex sets
J. Pach, G. Tóth: A generalization of the
Erdös-Szekeres theorem to disjoint convex sets, Discrete and
Computational Geometry 19 (1998), 437-445.
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J. Pach, G. Tóth: Erdös-Szekeres-type
theorems for segments and non-crossing convex sets,
Geometriae Dedicata 81 (2000), 1-12.
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G. Tóth: Finding convex sets in convex position,
Combinatorica 20 (2000), 589-596.
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