A 64-Rectangle Counterexample to Wegner's Conjecture and LP Gaps up to $5/2$

Aranya Kumar Bal

Wegner conjectured that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau (\mathcal{R})\le 2\nu (\mathcal{R})-1$, where $\nu$ is the packing number and $\tau$ is the p…