The board / graph theory / #920
Erdős Problem #920
SOLVEDdatabase updated 2025-08-31
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
\(f_k(n)\) is the maximum possible chromatic number of a graph with \(n\) vertices which contains no \(K_k\).
Is it true that, for \(k\geq 4\), \(f_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}}\) for some constant \(c_k>0\)? This problem follows immediately from Mattheus and Verstraete's lower bound [MaVe23] for k = 4 and Bradač's lower bound [Br26] for k ≥ 5.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/920.Prizenone
Topicsgraph theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/920
Attempts
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