Geometric Spanning Cycles in Bichromatic Point Sets

TL;DR

This paper investigates the existence of non-self-intersecting geometric spanning cycles in bichromatic point sets, ensuring each cycle's edges are crossed at most three times by the other, advancing understanding of geometric graph crossings.

Contribution

It introduces new bounds on crossings between bichromatic spanning cycles, providing constructions and proofs for crossing limitations in geometric graphs.

Findings

Red and blue spanning cycles exist with at most three crossings per edge.

The paper establishes bounds on crossings between bichromatic cycles.

New methods for constructing crossing-limited geometric cycles are presented.

Abstract

Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three times by the blue spanning cycle and vice-versa.