Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

EMPTY CONVEX 5-GONS IN PLANAR POINT SETS

  • Ann, Seong-Yoon (Department of Mathematics, Graduate School of Education, Chosun University) ;
  • Kang, En-Sil (Department of mathematics, College of Natural Sciences, Chosun University)
  • Received : 2009.07.03
  • Accepted : 2009.08.05
  • Published : 2009.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

Erd$\"{o}$s posed the problem of determining the minimum number g(n) such that any set of g(n) points in general position in the plane contains an empty convex n-gon. In 1978, Harborth proved that g(5) = 10. We reprove the result in a geometric approach.

Keywords

References

  1. P. Erdos, G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463-470
  2. H. Harborth, Konvexe Funfecke in ebenen Punktmengen, Elem. Math. 33(1978), 116-118
  3. J.D. Horton, Sets with no empty convex 7-gons, Canad. Math. Bull. 26 (1983), 482-484 https://doi.org/10.4153/CMB-1983-077-8
  4. J.D. Kalbfleisch, J.G. Kalbfleisch, R.G. Stanton, A combinatorial problem on convex regions, Proc. Louisiana Conf. Combinatorics, Graph Theory and Computing, Louisiana State Univ., Baton Rouge, La, 1970. Congr. Number I. (1970), 180-188
  5. W. Morris, V. Soltau. The Erdos-Szekeres problem on points in convex position - A survey, Bull. Amer. Math. Soc. 37 (2000), 437-458 https://doi.org/10.1090/S0273-0979-00-00877-6
  6. G. Toth, P. Valtr, Note on the Erdos-Szekeres Theorem, Discrete Comput. Geom. 19 (1998), 457-459 https://doi.org/10.1007/PL00009363
  7. G. Toth, P. Valtr, The Brdos-Szekeres theorem: upper bounds and related results, Combinatorial and Computational Geometry, 557-568. Math. Sci. Res. Inst. Publ. 52, Cambridge Univ. Press, Cambridge, 2005