Non-crossing geometric spanning trees with bounded degree and monochromatic leaves on bicolored point sets

12/07/2018

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by   Mikio Kano, et al.

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Let R and B be a set of red points and a set of blue points in the plane, respectively, such that R∪ B is in general position, and let f:R →{2,3,4, ...} be a function. We show that if 2< |B|<∑_x∈ R(f(x)-2) + 2, then there exists a non-crossing geometric spanning tree T on R∪ B such that 2<deg_T(x)< f(x) for every x∈ R and the set of leaves of T is B, where every edge of T is a straight-line segment.