Yao-Yao Graph a Spanner?

For an integer $k$, construct the directed Yao graph by retaining the shortest outgoing edge in each of $k$ equal cones at every point, then retain only the shortest incoming edge per cone and ignore orientations to obtain $YY_k$. Determine whether, for appropriate fixed $k$, there is a constant $t$ such that $YY_k$ is always a Euclidean $t$-spanner.