In this paper we show that the θ-graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ-graph for which it was not known whether its stretch factor was bounded.

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Keywords θ-graphs, computational geometry, geometric spanners
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Barba, L. (Luis), Bose, P, De Carufel, J.-L. (Jean-Lou), Van Renssen, A. (André), & Verdonschot, S. (Sander). (2013). On the stretch factor of the theta-4 graph. doi:10.1007/978-3-642-40104-6_10