  The classical no-three-in-line problem is to find the maximum number of
points that can be placed in the $n \times n$ grid so that no three points lie
on a line. Given a set $S$ of points in an Euclidean plane, the General
Position Subset Selection Problem is to find a maximum subset $S'$ of $S$ such
that no three points of $S'$ are collinear. Motivated by these problems, the
following graph theory variation is introduced: Given a graph $G$, determine a
largest set $S$ of vertices of $G$ such that no three vertices of $S$ lie on a
common geodesic. Such a set is a gp-set of $G$ and its size is the gp-number
${\rm gp}(G)$ of $G$. Upper bounds on ${\rm gp}(G)$ in terms of different
isometric covers are given and used to determine the gp-number of several
classes of graphs. Connections between general position sets and packings are
investigated and used to give lower bounds on the gp-number. It is also proved
that the general position problem is NP-complete.

Combinatorics