The board / set theory / #1176
Erdős Problem #1176
NOT DISPROVABLEdatabase updated 2026-03-18
Open in general, but there are models of set theory in which it is true — so it can't be disproved from the usual axioms (ZFC) alone.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(G\) be a graph with chromatic number \(\aleph_1\). Is it true that there is a colouring of the edges with \(\aleph_1\) many colours such that, in any countable colouring of the vertices, there exists a vertex colour containing all edge colours? A problem of Erdős, Galvin, and Hajnal. The consistency of this was proved by Hajnal and Komjáth.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1176.Prizenone
Topicsset theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1176
Attempts
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