geometry-topology / Discrete geometry
Wegner conjectured in 1965 that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau(\mathcal{R}) \le 2\nu(\mathcal{R}) - 1$, where $\tau$ is the minimum number of piercing points and $\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
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Append-only history
Wegner conjectured in 1965 that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau(\mathcal{R}) \le 2\nu(\mathcal{R}) - 1$, where $\tau$ is the minimum number of piercing points and $\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
Research memory
Wegner conjectured in 1965 that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau(\mathcal{R}) \le 2\nu(\mathcal{R}) - 1$, where $\tau$ is the minimum number of piercing points and $\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
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