Geodesic
On a Problem of Groübaum
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 23-25

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P n will denote a set of n points in the plane. A well known theorem of Gallai- Sylvester (see e.g. [4]) states that if the points of P n do not all lie on a line then they always determine an ordinary line, i.e. a line which goes through precisely two of the points of P n .Using this theorem I proved that if the points do not all lie on a line, they determine at least n lines. I conjectured that if n>n0 and no n—1 points of Pn are on a line, they determine at least 2n-4 lines. This conjecture was proved by Kelly and Moser [3], who, in fact, proved the following more general result: Let P n be such that at most n—k of its points are collinear. 
Erdös, P. On a Problem of Groübaum. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 23-25. doi: 10.4153/CMB-1972-005-4
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     title = {On a {Problem} of {Gro\"ubaum}},
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     doi = {10.4153/CMB-1972-005-4},
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