Abstract
A famous result of de Bruijn and Erdős (Indag. Math. 10 (1948) 421–423) states that a finite linear space has at least as many lines as points, with equality only if it is a projective plane or a near-pencil. This result led to the problem of characterizing finite linear spaces for which the difference between the number b of lines and the number v of points is assigned. In this paper finite linear spaces with b− v⩽ m, m being the minimum number of lines on a point, are characterized.
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