Geodesic
Sets with No Empty Convex 7-Gons
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 482-484

Voir la notice de l'article provenant de la source Cambridge University Press

Erdös has defined g(n) as the smallest integer such that any set of g(n) points in the plane, no three collinear, contains the vertex set of a convex n-gon whose interior contains no point of this set. Arbitrarily large sets containing no empty convex 7-gon are constructed, showing that g(n) does not exist for n≥l. Whether g(6) exists is unknown.
DOI : 10.4153/CMB-1983-077-8
Mots-clés : 52A40, Combinatorial geometry, convex polygon 
Horton, J. D. Sets with No Empty Convex 7-Gons. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 482-484. doi: 10.4153/CMB-1983-077-8
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[1] 1. Erdös, P. and Szekeres, G., A combinatorial problem in geometry, Compositio Math. 2 (1935), 463-470. Google Scholar

[2] 2. Erdös, P. and Szekeres, G., On some extremum problems in elementary geometry, Ann. Univ. Sci. Budapest 3–4 (1960-1) 53-62. Google Scholar

[3] 3. Harborth, H., Konvexe Funfecke in ebenen Punktmenger, Elem. Math. 33 (1978) 116-118. Google Scholar

[4] 4. Kalbfleisch, J. D., Kalbfleisch, J. G., and Stanton, R. G., A combinatorial problem on convex n-gons, Proc. Louisiana Conf. on Combinatorics Graph Theory, and Computing, Baton Rouge (1970), 180-188. Google Scholar

[5] 5. Moser, Wm., Research Problems in Geometry, McGill University, (1981) #29. Google Scholar

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