Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

There are some points in the plane and some of them are connected with segments between them. We look at this structure as a graph implemented into the plane where the points are the vertices and the segments are the edges. We search for a maximum matching with no edges intersecting each other.

Is there any results about this question - NP-hardness or algortihm or characterisation even for some cases (the one case I see is when the graph is bipartite and the vertices of the two classes are on two parallel lines respectively)?

Thanks for the answers

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Perhaps the in-press 2012 paper, "Non-crossing matchings of points with geometric objects," by Aloupis et al. (Elsevier link; Prelim. PDF link) will help, either directly or through its references. (I have only passing familiarity with the contents of this paper myself.)
           Figure 1

share|improve this answer
Thanks! This paper seems just what I looked for. –  David Herskovics Jul 7 '12 at 16:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.