Geodesic
Touching Convex Sets in the Plane
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 495-504

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DOI

Two subsets of the Euclidean plane touch each other if they have a point in common and there is a straight line separating one from the other.It is shown that there exists a positive constant c such that if are families of plane convex sets with for some k ≥ 1 and if every touches every then either contains k members having nonempty intersection.
DOI : 10.4153/CMB-1994-072-1
Mots-clés : 52A10, convex sets 
Katchalski, Meir; Pach, János. Touching Convex Sets in the Plane. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 495-504. doi: 10.4153/CMB-1994-072-1
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     title = {Touching {Convex} {Sets} in the {Plane}},
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     year = {1994},
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     doi = {10.4153/CMB-1994-072-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-072-1/}
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