Simple alternating path problem

Let A be a set of 2n points in general position on a plane, and suppose n of the points are coloured red while the remaining are coloured blue. An alternating path P of A is a sequence p1, p2,..., p2n of points of A such that p2i is blue and p2i+1 is red. P is simple if it does not intersect itself. We determine the condition under which there exists a simple alternating path P of A for the case when the 2n points are the vertices of a convex polygon. As a consequence an O(n2) algorithm to find such an alternating path (if it exists) is obtained. This research was supported under Natural Sciences and Engineering Research Council of Canada (NSERC Canada) grant number A0977.