Erdős 836: vertex counts and pairwise edge intersections in 3-chromatic intersecting uniform hypergraphs
A complete Lean 4 resolution of both parts of Erdős problem 836 (posed by Erdős and Shelah; Erdős and Lovász, 1975) on 3-chromatic intersecting r-uniform hypergraphs, together with structural bounds on the Erdős–Shelah codimension-one avoidance question. For Part (i), it formalizes Noga Alon's equitable-partition construction with (2r - 2) + C(2r - 2, r - 1) / 2 active vertices to disprove the O(r²) vertex bound for all r ≥ 2. For Part (ii), it adapts and generalizes Liam Price's minimal-blue bipartite double-counting argument to prove the universal bound r ≤ 2t + 1 when distinct edges meet…
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