1) V1 Is there an absolute c>0 such that every intersecting r-uniform hypergraph of chromatic number exactly three has two distinct edges meeting in at least cr vertices?
open, filed Tue Aug 25 2026 07:33:54 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The Fano hypergraph kernel-checks uniformity, intersection, and an explicit proper 3-coloring; exact non-2-colorability is standard prior art. An independent encoding is definitionally equal and nine content-free bridges fail. Whole routes cover Erdős–Lovász covering scales, minimal non-2-colorable cores, codegree averaging, delta systems, Fano/projective blow-ups, and random refutations.
Scope. The unresolved second question in Erdős problem 836. Uniformity, pairwise intersection, exact chromatic number three (3-colorable but not 2-colorable), distinct witness edges, and a uniform positive linear constant are explicit.