Abstract
The Erdös-Szekeres k-gon theorem [1] says that for any integer k ≥ 3 there is an integer n(k) such that any set of n(k) points in the plane, no three on a line, contains k points which are vertices of a convex k-gon. It is a classical result both in combinatorial geometry and in Ramsey theory. Sometimes it is called the Happy End(ing) Theorem (a name given by Paul Erdös), since George Szekeres later married Eszter Klein who proposed a question answered by the theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compos. Math. 2, 463–470 (1935)
Erdős, P., Szekeres, G.: On some extremum problems in elementary geometry. Ann. Univ. Sci. Bp. Rolan do Eötvös Nomin., Sect. Math. 3/4, 53–62 (1960–1961)
Szekeres, G., Peters, L.: Computer solution to the 17-point Erdős-Szekeres problem. ANZIAM Journal 48, 151–164 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Valtr, P. (2014). The Happy End Theorem and Related Results. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-04657-0_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04656-3
Online ISBN: 978-3-319-04657-0
eBook Packages: Computer ScienceComputer Science (R0)