The board / graph theory / #554
Erdős Problem #554
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Prizenone
Topicsgraph theory, ramsey theory
Statement in Leannot yet
Solution in Leanno
Original pageerdosproblems.com/554
Attempts
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The live problem is open with no claimant or worker; current bounds miss by a \(k^{k/\ell}\) factor, and the report proves a precise colour-index-gap reduction plus fully checked finite certificates,
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