• Corpus ID: 119637536

Upper bounds for the piercing number of families of pairwise intersecting convex polygons

@article{Katchalski2011UpperBF,
  title={Upper bounds for the piercing number of families of pairwise intersecting convex polygons},
  author={Meir Katchalski and D. Nashtir},
  journal={arXiv: Metric Geometry},
  year={2011}
}
A convex polygon $A$ is related to a convex $m$-gon $K= \bigcap_{i=1}^m k_i^+$, where $k_1^+,..., k_m^+$ are the $m$ halfplanes whose intersection is equal to $K$, if $A$ is the intersection of halfplanes $a_1^+,...,a_l$, each of which is a translate of one of the $k_i^+$-s. The planar family ${\cal A}$ is related to $K$ if each $A \in {\cal A}$ is related to $K$. We prove that any family of pairwise intersecting convex sets related to a given $n$-gon has a finite piercing number which depends… 

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