1) V1 Is there a graph on a well-ordered vertex set of order type omega_2 squared, with chromatic number aleph_2, such that every induced subgraph on a vertex set of strictly smaller order type is countably colorable?
open, filed Tue Aug 25 2026 10:18:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Every Jig problem through 364 was covered: direct pulls through 362 had already been semantically reviewed, and the two later roots 363 and 364 were opened and are unrelated. The exact writer, eleven red/restatement controls, independent expansion of chromatic exactness, a countably-colorable boundary witness, and the construction/nonexistence burdens compile. Whole-root attacks used the Erdős--Hajnal coordinate-order graph, square/lexicographic variants, edge thinning, transfinite recursion, and the opposite extraction route. The standard omega-two construction gives only an aleph-one upper bound on smaller-type subgraphs; lowering this uniformly to aleph-zero while retaining global chromatic number aleph-two is the exact open obstruction.
Scope. First question only; well-orders of exact type omega_2 squared; global chromatic number exactly aleph_2; every induced smaller-order-type subgraph has chromatic number at most aleph_0.