Optimal 3D Angular Resolution for Low-Degree Graphs

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.

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