Mathematics – Combinatorics
Scientific paper
2011-07-12
Mathematics
Combinatorics
Scientific paper
We study the following problem - How many arbitrary edges can be removed from a complete geometric graph with 2n vertices such that the resulting graph always contains a perfect non-crossing matching? We first address the case where the boundary of the convex hull of the original graph contains at most $n + 1$ points. In this case we show that n edges can be removed, one more than the general case. In the second part we establish a lower bound for the case where the $2n$ points are randomly chosen. We prove that with probability which tends to 1, one can remove any $n + \Theta(n/log (n))$ edges but the residual graph will still contain a non-crossing perfect matching. We also discuss the upper bound for the number of arbitrary edges one must remove in order to eliminate all the non-crossing perfect matchings.
No associations
LandOfFree
Edge-Removal and Non-Crossing Perfect Matchings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Edge-Removal and Non-Crossing Perfect Matchings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Edge-Removal and Non-Crossing Perfect Matchings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565596