Before revision:  Let M be a perfect matching between points from R and B, using n straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint. We forbid line segments to cross. Denote the length of a longest line segmentin M with bn(M), which we also call the of M.
After revision:  Let M be a perfect matching between points from R and B, using n straight line segments so that the segments do not cross. Bottleneck matching is such a matching that minimizes the length of a longest line segmentin M with bn(M), which we also call the of M.