Geodesic
Sets in the plane with many concyclic subsets
The electronic journal of combinatorics, Tome 12 (2005)
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We study sets of points in the Euclidean plane having property $R(t,s)$: every $t$-tuple of its points contains a concyclic $s$-tuple. Typical examples of the kind of theorems we prove are: a set with $R(19,10)$ must have all its points on two circles or all its points, with the exception of at most 9, are on one circle; of a set with $R(8,5)$ and $N\geq 28$ points at least $N-3$ points lie on one circle; a set of at least 109 points with $R(7,4)$ has $R(109,7)$. We added some results on the analogous configurations in 3-space.
DOI : 10.37236/1938
Classification : 05B30, 51M04
Mots-clés : round, block design, Ramsey numbers 
@article{10_37236_1938,
     author = {R. H. Jeurissen},
     title = {Sets in the plane with many concyclic subsets},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1938},
     zbl = {1076.05019},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1938/}
}
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R. H. Jeurissen. Sets in the plane with many concyclic subsets. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1938

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