  In this paper we prove that $Y_5$, the Yao graph with five cones, is a
spanner with stretch factor $\rho = 2+\sqrt{3} \approx 3.74$. Since $Y_5$ is
the only Yao graph whose status of being a spanner or not was open, this
completes the picture of the Yao graphs that are spanners: a Yao graph $Y_k$ is
a spanner if and only if $k \geq 4$.
  We complement the above result with a lower bound of 2.87 on the stretch
factor of $Y_5$. We also show that $YY_5$, the Yao-Yao graph with five cones,
is not a spanner.

Computational Geometry