RAC Drawings of Graphs with Low Degree

TL;DR

This paper advances the understanding of RAC graph drawings by proving that various classes of low-degree graphs, including degree-3, degree-4, and degree-7 graphs, can be drawn with right-angle crossings under different bend constraints.

Contribution

It extends known results by showing that all 3-edge-colorable degree-3 graphs admit straight-line RAC drawings, degree-4 graphs with one bend per edge do as well, and degree-7 graphs with two bends per edge are also drawable.

Findings

Degree-3 graphs with Hamiltonian cycles admit straight-line RAC drawings.

Degree-4 graphs with one bend per edge admit RAC drawings.

Degree-7 graphs with seven-edge-coloring admit RAC drawings with two bends per edge.

Abstract

Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable representations of non-planar graphs by supporting the optimal case in which all crossings form 90{\deg} angles. In this work, we make progress on the problem of finding RAC drawings of graphs of low degree. In this context, a long-standing open question asks whether all degree-3 graphs admit straight-line RAC drawings. This question has been positively answered for the Hamiltonian degree-3 graphs. We improve on this result by extending to the class of 3-edge-colorable degree-3 graphs. When each edge is allowed to have one bend, we prove that degree-4 graphs admit such RAC drawings, a result which was previously known only for degree-3 graphs. Finally, we show that 7-edge-colorable degree-7 graphs admit RAC drawings with two bends per edge. This improves over the previous result on degree-6 graphs.