The board / graph theory / #762
Erdős Problem #762
DISPROVED LEANdatabase updated 2026-02-08
The statement as posed is false. A solution has also been checked by machine, in Lean.
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The cochromatic number of \(G\), denoted by \(\zeta(G)\), is the minimum number of colours needed to colour the vertices of \(G\) such that each colour class induces either a complete graph or empty graph. Is it true that if \(G\) has no \(K_5\) and \(\zeta(G)\geq 4\) then \(\chi(G) \leq \zeta(G)+2\)? This has been disproved by Steiner [St24b], who constructed a graph \(G\) with \(\omega(G)=4\), \(\zeta(G)=4\), and \(\chi(G)=7\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/762.Prizenone
Topicsgraph theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/762
Attempts
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