On certain geometric properties of the YaoYao graphs
We show that, for any constant \(\rho > 1\), there exists an integer constant \(k\) such that the YaoYao graph with parameter \(k\) defined on a civilized unit disk graph is a geometric spanner of stretch factor \(\rho \). This improves the results of Wang and Li in several aspects, as described in the paper. This partially answers an open problem posed by Demaine, Mitchell and ORourke about the spanner properties of YaoYao graphs. We also show that the YaoYao graph with parameter \(k=4\) defined on the complete Euclidean graph is not plane.
yaoyao graphs unit disk graphs spanners yao graphs