Optimal 3D angular resolution for low-degree graphs

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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° 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° angles, i.e., the angular resolution of the diamond lattice, between any two edge segments meeting at a vertex or bend. © 2011 Springer-Verlag.

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Eppstein, D., Löffler, M., Mumford, E., & Nöllenburg, M. (2011). Optimal 3D angular resolution for low-degree graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6502 LNCS, pp. 208–219). https://doi.org/10.1007/978-3-642-18469-7_19

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