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# A GENERAL POSITION PROBLEM IN GRAPH THEORY

## Abstract

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 $\text{gp}(G)$ of $G$ . Upper bounds on $\text{gp}(G)$ 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.

## Footnotes

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This work was supported and funded by Kuwait University, Research Project No. QI 02/17.

## References

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# A GENERAL POSITION PROBLEM IN GRAPH THEORY

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