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Reconfirmation of Two Results on Disjoint Empty Convex Polygons

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Discrete Geometry, Combinatorics and Graph Theory (CJCDGCGT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4381))

Abstract

For k ≥ 3, let m(k,k + 1) be the smallest integer such that any set of m(k,k + 1) points in the plane, no three collinear, contains two different subsets Q 1 and Q 2, such that CH(Q 1) is an empty convex k −gon, CH(Q 2) is an empty convex (k + 1) −gon, and CH(Q 1) ∩ CH(Q 2) = ∅, where CH stands for the convex hull. In this paper, we revisit the case of k = 3 and k = 4, and provide new proofs.

This research was supported by National Natural Science Foundation of China 10571042, NSF of Hebei A2005000144 and the Science Foundation of Hebei Normal University.

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References

  1. Erdős, P.: On some problems of elementary and combinatorial geometry. Ann. Mat. Pura. Appl. 103(4), 99–108 (1975)

    MathSciNet  Google Scholar 

  2. Erdős, P., Szekeres, G.: A combinatorial problem in geometry. Compositio Math. 2, 463–470 (1935)

    MathSciNet  Google Scholar 

  3. Harborth, H.: Konvexe Fünfecke in ebenen Punktmengen. Elem. Math. 33, 116–118 (1978)

    MATH  MathSciNet  Google Scholar 

  4. Horton, J.D.: Sets with no empty convex 7-gon. Canad. Math.Bull. 26, 482–484 (1983)

    MATH  MathSciNet  Google Scholar 

  5. Hosono, K., Urabe, M.: On the number of disjoint convex quadrilaterals for a planar point set. Computational Geometry 20, 97–104 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Urabe, M.: On a partition into convex polygons. Discrete Applied Mathematics 64, 179–191 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hosono, K., Urabe, M.: On the Minimum Size of a Point Set Containing Two Non-intersecting Empty Convex Polygons. In: Akiyama, J., Kano, M., Tan, X. (eds.) JCDCG 2004. Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004. LNCS, vol. 3742, pp. 117–122. Springer, Heidelberg (2005)

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Authors and Affiliations

  1. College of Physical Science and Technology, Hebei University, Baoding 071002, China

    Liping Wu

  2. College of Mathematics, Hebei Normal University, Shijiazhuang, 050016, China

    Ren Ding

Authors
  1. Liping Wu
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  2. Ren Ding
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Editor information

Jin Akiyama William Y. C. Chen Mikio Kano Xueliang Li Qinglin Yu

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© 2007 Springer Berlin Heidelberg

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Wu, L., Ding, R. (2007). Reconfirmation of Two Results on Disjoint Empty Convex Polygons. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_23

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  • DOI: https://doi.org/10.1007/978-3-540-70666-3_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70665-6

  • Online ISBN: 978-3-540-70666-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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