In this paper, we show that the θ-graph with three cones is connected. We also provide an alternative proof of the connectivity of the Yao graph with three cones.

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Keywords Connected networks, Spanning graphs, Theta graphs, Yao graphs
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Journal Computational Geometry
Aichholzer, O. (Oswin), Bae, S.W. (Sang Won), Barba, L. (Luis), Bose, P, Korman, M. (Matias), Van Renssen, A. (André), … Verdonschot, S. (Sander). (2014). Theta-3 is connected. Computational Geometry, 47(9), 910–917. doi:10.1016/j.comgeo.2014.05.001