Monochromatic geometric k-factors for bicolored point sets with auxiliary points

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S. Draw monochromatic geometric k-factors of bicolored point sets using auxiliary points.We use two types of auxiliary points: Steiner points and white points.We provide algorithms for constructing those k-factors.We give bounds on the number of auxiliary points needed.