1) V1 Let f(k,7) be the least universal size of a transversal for a k-uniform finite family whenever each seven-member subfamily has a transversal of size at most two.
open, filed Tue Aug 25 2026 06:57:15 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Is f(k,7)=(3/4+o(1))k?
The writer's initial exact-two reading was rejected against the original review and corrected to at-most-two before posing. Empty and singleton families kernel-check boundary behavior; an independent encoding is definitionally equal; nine content-free bridges fail. Whole attacks cover minimal-counterexample/private-edge structure, averaging, LP duality and rounding, delta systems/shifting, and geometric/cyclic counterexamples.
Scope. The first precise conjecture in Erdős problem 644. Families and their finite ground sets are quantified universally. Local transversals have size at most two, matching the original t=2 formulation; the global extremal bound is the least natural universal bound.