The minimum number of edges meeting all triangles is at most twice the maximum number of edge-disjoint triangles.

Statement

For every graph $G$, $\tau_{\triangle}(G) \le 2\,\nu_{\triangle}(G)$: the triangle edge-cover number is at most twice the triangle packing number.

Assessment

Renown 3/5

A benchmark problem in extremal combinatorics; the constant 2 is tight for K4 and K5.

Attackability 2/5

Finite witness with LP/ILP oracles; fractional version proved (Krivelevich), 2.87 bound known, tight examples (K4, K5) are natural seeds but decades of attention have found no violation.

finite witness

5/5

oracle cost

3/5

freshness

1/5

seedability

3/5

Claims

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