B ar any, I., and Valtr, P. A positive fraction Erd}os-Szekeres theorem. Discrete Comput. Geom. 19, 3, Special Issue (1998), 335-342. Home/Search Document Not in Database Summary Related Articles Check |
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Canonical Theorems for Convex Sets - Pach, Solymosi (1998) (1 citation) (Correct)
....many r tuples in convex position. For instance, Solymosi [S] showed that for a suitable constant c r 0, one can select a sequence of c r n distinct elements from P , whose any r consecutive members are in convex position. In the case r = 4, Nielsen [N] and, in general, B ar any and Valtr [BV] proved the following stronger result. Theorem A. For any xed r 4, there is a constant c r 2 satisfying the following condition. Every n element point set P in general position in the plane has r pairwise disjoint subsets P i (1 i r) such that jP i j bc r nc and no matter how we ....
....i r) such that no matter how we pick one set from each F i , they are always in convex position. It is worth mentioning that in the special case when all members of F are single points, our proof shows that the statement of Theorem A is true with a much better constant c r than the one given in [BV]. The proofs of the next three theorems follow the same scheme. A polygonal path p 1 p 2 : p r in the plane or in space, is called straight if p i 1 p i p i 1 ; 1 i r (cf. ES2] P] The length of a polygonal path is the number of its vertices. Theorem 2. For every d 2; r ....
I. Barany and P. Valtr, A positive fraction Erd}os-Szekeres theorem, Discrete and Computational Geometry, this issue.
The Erdös-Szekeres theorem: upper bounds and related results - Toth, Valtr (2004) Self-citation (Valtr) (Correct)
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I. Barany and P. Valtr, A positive fraction Erd}os{Szekeres theorem, Discrete and Computational Geometry 19 (1998), 335-342.
On the Partitioned Version of the Erdös-Szekeres Theorem - Por, Valtr (2002) Self-citation (Valtr) (Correct)
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I. Barany and P. Valtr, A positive fraction Erd}os{Szekeres theorem, Discrete and Computational Geometry 19 (1998), 335-342.
Ramsey Theory Applications - Vera Rosta Dept (Correct)
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B ar any, I., and Valtr, P. A positive fraction Erd}os-Szekeres theorem. Discrete Comput. Geom. 19, 3, Special Issue (1998), 335-342.
An Erdös-Szekeres type problem in the plane - Karolyi, Toth (Correct)
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I. Barany and P. Valtr, A positive fraction Erd}os-Szekeres theorem, Discrete and Computational Geometry 19 (1998), 335-342.
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