A GENERAL POSITION PROBLEM IN GRAPH THEORY

The paper introduces a graph theory variation of the general position problem: 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 max-gp-set of G and its size is the gp-number gp(G) of G. Upper bounds on 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.