Aranya Kumar Bal

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

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 piercing number. Ajwani, Gajjala, Raman, and Ray recently disproved this by constructing a triangle-free counterexample on $2196\cd...