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

• Published in: Information processing letters Vol. 114; no. 1-2; pp. 19 - 24
• Main Authors: Garijo, D., Garrido, M.A., Grima, C.I., Márquez, A., Moreno-González, A., Portillo, J.R., Reyes, P., Robles, R., Valenzuela, J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2014; Elsevier Sequoia S.A
• Subjects: Algorithms; Computational geometry; Computer science; Construction; Data processing; Geometry; Graph algorithms; Graph coloring; k-factors; Mathematical problems; Red–blue point sets; Steiner points; Studies; k-factors; Computational geometry; Red–blue point sets; Steiner points
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2013.10.002

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.