Table of Contents
ISRN Geometry
Volume 2013 (2013), Article ID 328095, 6 pages
http://dx.doi.org/10.1155/2013/328095
Research Article

On the Existence of a Point Subset with 3 or 6 Interior Points

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani 12121, Thailand

Received 11 September 2013; Accepted 31 October 2013

Academic Editors: S. Hernández, A. Stipsicz, and S. Troubetzkoy

Copyright © 2013 Banyat Sroysang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Erdős and G. Szekeres, “A combinatorial problem in geometry,” Compositio Mathematica, vol. 2, pp. 463–470, 1935. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Erdős and G. Szekeres, “On some extremum problems in elementary geometry,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, vol. 3-4, pp. 53–62, 1961. View at Google Scholar · View at MathSciNet
  3. W. E. Bonnice, “On convex polygons determined by a finite planar set,” The American Mathematical Monthly, vol. 81, pp. 749–752, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. D. Kalbfleisch, J. G. Kalbfleisch, and R. G. Stanton, “A combinatorial problem on convex n-gons,” in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory, and Computing, pp. 180–188, 1970.
  5. G. Szekeres and L. Peters, “Computer solution to the 17-point Erdős-Szekeres problem,” The ANZIAM Journal, vol. 48, no. 2, pp. 151–164, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Avis, K. Hosono, and M. Urabe, “On the existence of a point subset with a specified number of interior points,” Discrete Mathematics, vol. 241, no. 1–3, pp. 33–40, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Wei and R. Ding, “More on planar point subsets with a specified number of interior points,” Mathematical Notes, vol. 83, no. 5-6, pp. 684–687, 2008. View at Publisher · View at Google Scholar
  8. X. Wei and R. Ding, “More on an Erdős-Szekeres-type problem for interior points,” Discrete & Computational Geometry, vol. 42, no. 4, pp. 640–653, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. Sroysang, “A lower bound for Erdős-Szekeres-type problem with interior points,” International Journal of Open Problems in Computer Science and Mathematics, vol. 4, no. 4, pp. 68–73, 2011. View at Google Scholar
  10. B. Sroysang, “An improved lower bound for an Erdős-Szekeres-type problem with interior points,” Applied Mathematical Sciences, vol. 6, no. 69–72, pp. 3453–3459, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. Avis, K. Hosono, and M. Urabe, “On the existence of a point subset with 4 or 5 interior points,” in Discrete and Computational Geometry, vol. 1763 of Lecture Notes in Computer Science, pp. 57–64, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Wei and R. Ding, “A note on point subset with 5 or 6 interior points,” Southeast Asian Bulletin of Mathematics, vol. 33, no. 6, pp. 1207–1214, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Wei, W. Lan, and R. Ding, “On the existence of a point subset with three or five interior points,” Mathematical Notes, vol. 88, no. 1-2, pp. 103–111, 2010. View at Publisher · View at Google Scholar
  14. B. Sroysang, “On the existence of a point subset with 3 or 7 interior points,” Applied Mathematical Sciences, vol. 6, no. 129–132, pp. 6593–6600, 2012. View at Google Scholar · View at MathSciNet
  15. B. Sroysang, “Remarks on point subset with 3 or 3+n interior points,” Advances and Applications in Mathematical Sciences, vol. 10, no. 6, pp. 627–630, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet