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We show that each set of n 2 points in the plane in general position has a straight-line matching with at least (5n+1) /27 edges whose segments form a connected set, and such a matching can be computed in O (n n) time. As an upper bound, we show that for some planar point sets in general position the largest matching whose segments form a connected set has n-13 edges. We also consider a colored version, where each edge of the matching should connect points with different colors.
Aichholzer et al. (Mon,) studied this question.