Optimal 3D Angular Resolution for Low-Degree Graphs

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.

18 pages, 10 figures. Extended version of paper to appear in Proc. 18th Int. Symp. Graph Drawing, Konstanz, Germany, 2010