The board / graph theory / #61
Erdős Problem #61
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).
The Erdős–Hajnal Conjecture states that there is a constant \(c(H) > 0\) for each \(H\) such that we can take \(f(n) = n^{c(H)}\) in the above formulation.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/61.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/61
Attempts
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Explicit induced-C6-free lexicographic powers have 17^k vertices and homogeneous number 3^k, giving c_EH(C6) <= log_17(3), with T_C6(4)=18 and an exact 104-type six-vertex threshold table; the uniform
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