The board / graph theory / #1104
Erdős Problem #1104
OPENdatabase updated 2025-10-26
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).
Maximum chromatic number of a triangle-free graph on `n` vertices.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1104.Prizenone
Topicsgraph theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA292528
Original pageerdosproblems.com/1104
Attempts
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Independently verified \(h_3(4)=11\), \(h_3(5)\ge19\), and exact \(f(n)\) through \(n=18\); proved the Davies--Illingworth threshold/peeling template cannot beat constant \(2\), but did not improve th
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