Open Research Index

Erdős Problem 625: chromatic versus cochromatic number of a random graph

Samuil Petkov

Palomar Registrypalomar/PALOMAR-2026-09-02-000006Sep 2, 2026math.COscore 0

A Lean 4 formalization of the full-sequence quantitative theorem for G(n,1/2): with probability tending to one, the chromatic number minus the cochromatic number is at least ((log 2)^2/4) log(200/153) times n/(log n)^3. The formal statement uses the finite binomial random-graph measure, natural-valued chromatic and cochromatic numbers, real subtraction, and convergence along all natural n.

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