Drawing non-planar graphs with rotation systems on the Klein bottle

TL;DR

This paper presents a linear-time algorithm for drawing non-planar graphs on the Klein bottle without crossings, given a rotation system, advancing graph visualization on non-orientable surfaces.

Contribution

It introduces a linear-time algorithm for straight-line drawings of non-planar graphs on the Klein bottle using rotation systems, a novel approach for such surfaces.

Findings

Algorithm runs in linear time relative to edges

Produces crossing-free straight-line drawings on the Klein bottle

Applicable to simple 3-connected non-planar graphs

Abstract

This paper provides a linear time algorithm in the number of edges that, given a simple 3-connected non-planar graph G with a Klein bottle rotation system, outputs a straight line drawing of G with no crossings on the flat Klein bottle.