CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

Let ${\delta }_0\left(P,k\right)$ denote the degree $k$ dilation of a point set $P$ in the domain of plane geometric spanners. If $\Lambda$ is the infinite square lattice, it is shown that $1+\sqrt{2}\le {\delta }_0\left(\Lambda ,3\right)\le \left(2\sqrt{2}+3\right)5^{-1∕2}=2.6065\dots$ and ${\delta }_0\left(\Lambda ,4\right)=\sqrt{2}$. If $\Lambda$ is the infinite hexagonal lattice, it is shown that ${\delta }_0\left(\Lambda ,3\right)=1+\sqrt{3}$ and ${\delta }_0\left(\Lambda ,4\right)=2$.

This is joint work with Anirban Ghosh (University of Wisconsin-Milwaukee).