A graph whose vertex set is a set P of points in the plane and whose edges are line segments joining pairs of elements of P is called a geometric graph. In this paper we survey several results on geometric graphs on colored point sets. Of particular interest are bicolored point sets \(P= R \cup B\) in which the elements of P can considered to be colored red or blue. We will pay particular attention to perfect matchings, spanning trees and paths whose vertex sets are colored point sets. In the last section of this paper we give some results on point sets whose elements are labelled with the integers \(\{1, \ldots , n\}\) such that different elements of P receive different labels.

On Geometric Graphs on Point Sets in the Plane

A note on two geometric paths with few crossings for points labeled by integers in the plane

http://www.math.unam.mx/%7Eurrutia/online_papers/harmonic.pdf

A note on harmonic subgraphs in labelled geometric graphs

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A note on harmonic subgraphs in labelled geometric graphs