Erdős Problem #597
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The graph-target ordinal partition relation \(\alpha \to (\beta, G)^2\): for every red/blue colouring of the edges of the complete graph on \(\alpha\), either there is a red clique of order type \(\beta\), or there is a blue copy of the graph \(G\) (an injective map sending the edges of \(G\) to blue edges). This generalises `OrdinalCardinalRamsey`, replacing the blue clique of cardinality \(c\) (i.e. a blue copy of \(K_c\)) by a blue copy of an arbitrary graph \(G\). Will be moved to `FormalConjecturesForMathl
Attempts
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proved \(\omega_1^2\to(\omega_1\omega,G)^2\) for every finite \(K_4\)-free block graph and reduced the full finite question exactly to 2-connected \(K_4\)-free blocks; the first unresolved-by-this-met
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