A Counterexample to Wegner's Conjecture for Axis-Parallel Rectangles (opens in new tab)

In 1965, Wegner conjectured that every finite family \(\mathcal R\) of axis-parallel rectangles in the plane satisfies \(\tau(\mathcal R) \le 2\nu(\mathcal R)-1\), where \(\tau(\mathcal R)\) denotes the minimum number of points needed to pierce all rectangles in \(\mathcal R\), and \(\nu(\mathcal R)\) denotes the maximum size of a pairwise disjoint subfamily. Over the last six decades, the conjecture has motivated a long line of work: it has bee...