Optimal 3D Angular Resolution for Low-Degree Graphs

TL;DR

This paper investigates optimal 3D angular resolutions for low-degree graphs, demonstrating specific bend and angle constraints for graphs with maximum degrees three and four, enhancing 3D graph drawing techniques.

Contribution

It establishes new bounds on bends and angles for 3D drawings of low-degree graphs, improving understanding of their geometric representations.

Findings

Graphs of max degree 3 can be drawn with 2 bends per edge and 120-degree angles.

Graphs of max degree 4 can be drawn with 3 bends per edge and 109.5-degree angles.

Provides constructive methods for achieving these drawings.

Abstract

We show that every graph of maximum degree three can be drawn in three dimensions with at most two bends per edge, and with 120-degree angles between any two edge segments meeting at a vertex or a bend. We show that every graph of maximum degree four can be drawn in three dimensions with at most three bends per edge, and with 109.5-degree angles, i.e., the angular resolution of the diamond lattice, between any two edge segments meeting at a vertex or bend.