On the Number of Edges in Maximally Linkless Graphs

A maximally linkless graph is a graph that can be embedded in ${\mathbb{R}}^3$ without any links, but cannot be embedded in such a way if any other edge is added to the graph. Recently, a family of maximally linkless graphs was found with $m=3n-3$ edges. We improve upon this by demonstrating a new family of maximally linkless graphs with $m\le \frac{14}{5}n$ edges.