Linear spaces on \(v\) points with \(v-3\) mutually intersecting long lines (Q1179837)

A linear space \(S=(P,L)\) is a system of points \(P\) and lines \(L\) such that any line has at least two points, and two distinct points are on precisely one line. We only consider linear spaces with a finite number of points and lines. The number of points is denoted by \(v\). For a line \(r\), \(v(r)\) will be the number of points on \(r\). A long line is a line \(r\) such that \(v(r)=\max\{v(s): s\in L\}\). Finite linear spaces with \(v-3\) mutually intersecting long lines are completely characterized.