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Maximal knotless graphs
A graph is maximal knotless if it is edge maximal for the property of knotless embedding in $R^3$. We show that such a graph has at least $\frac74 |V|$ edges, and construct an infinite family of maximal knotless graphs with $|E| < \frac52|V|$. With the exception of $|E| = 22$, …