Spanning Trees of Multicoloured Point Sets with Few Intersections
نویسندگان
چکیده
Kano et al. proved that if P0, P1, . . . , Pk−1 are pairwise disjoint collections of points in general position, then there exist spanning trees T0, T1, . . . , Tk−1, of P0, P1, . . . , Pk−1, respectively, such that the edges of T0 ∪ T1 ∪ · · · ∪ Tk−1 intersect in at most (k − 1)n − k(k − 1)/2 points. In this paper we show that this result is asymptotically tight within a factor of 3/2. To prove this, we consider alternating collections, that is, collections such that the points in P := P0 ∪P1 ∪ · · · ∪Pk−1 are in convex position, and the points of the Pi’s alternate in the convex hull of P .
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On spanning trees and cycles of multicolored point sets with few intersections
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