Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

THE LOWER BOUND OF THE NUMBER OF NON-OVERLAPPING TRIANGLES

  • Xu, Changqing (Department of Mathematics, Hebei Normal University) ;
  • Ding, Ren (Department of Mathematics, Hebei Normal University)
  • Published : 2003.01.01

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Abstract

Andras Bezdek proved that if a convex n-gon and n points are given, then the points and the sides of the polygon can be renumbered so that at least[${\frac{n}{3}}$] triangles spanned by the ith point and the ith side (i = 1,2,...n) are mutually non-overlapping. In this paper, we show that at least [${\frac{n}{2}}$] mutually non-overlapping triangles can be constructed. This lower bound is best possible.

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References

  1. Geometriae Dedicata v.80 Covering a convex polygon by triangles Angras Bezdek
  2. Math. Notes v.44 Covering a convex polygon by triangles with fixed vertices A. V. Bogomolnaya;F. L. Nazarov;S. E. Rukshin
  3. Korean J. Comput. and Appl. Math. v.5 A new parallel algorithm for rooting a tree Taenam Kim;Dukhwan Oh;Eunki Lim
  4. Korean J. Comput. and Appl. Math. v.5 Classifivation of association schemes with 18 and 19 vertices A. Hanaki;I. Miyamoto