Discrete Geometry on Red and Blue Points in the Plane Lattice

Mikio Kano () and Kazuhiro Suzuki ()
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Mikio Kano: Ibaraki University, Department of Computer and Information Sciences
Kazuhiro Suzuki: Kochi University, Department of Information Science

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 355-369 from Springer

Abstract: Abstract We consider some problems on red and blue points in the plane lattice. An L-line segment in the plane lattice consists of a vertical line segment and a horizontal line segment having a common endpoint. There are some results on geometric graphs on a set of red and blue points in the plane. We show that some similar results also hold for a set of red and blue points in the plane lattice using L-line segments instead of line segments. For example, we show that if n red points and n blue points are given in the plane lattice in general position, then there exists a noncrossing geometric perfect matching covering them, each of whose edges is an L-line segment and connects a red point and a blue point.

Keywords: Span Tree; General Position; Plane Lattice; Left Edge; Bottom Edge (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_18

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DOI: 10.1007/978-1-4614-0110-0_18

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