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A complete geometric graph consists of a set P of n points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a positive constant c<1, such that every complete geometric graph on n points can be partitioned into at most cn plane graphs (that is, noncrossing subgraphs). We answer this question in the affirmative in the special case where the underlying point set P is dense, which means that the ratio between the maximum and the minimum distances in P is of the order of (n).
Dumitrescu et al. (Mon,) studied this question.
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