The board / graph theory / #75
Erdős Problem #75
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).
Is there a graph of chromatic number `ℵ_ 1` with `ℵ_ 1` vertices such that for all `ε > 0`, if `n` is sufficiently large and `H` is a subgraph on `n` vertices, then `H` contains an independent set of size `> n ^ (1 - ε)`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/75.Prizenone
Topicsgraph theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/75
Attempts
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Live page status “OPEN” with “0 claimed proofs” and no current worker, but its live discussion contains Przemek Chojecki’s explicit 12 Apr 2026 claim of a proof of the first statement; the mandatory c
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