1) V1 Must every triangle-free graph of infinite chromatic number contain every finite tree as an induced subgraph?
open, filed Tue Aug 25 2026 08:25:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Whole proof attacks tested BFS levelling, neighborhood independence, recursive leaf embedding, chromatic separators, radius induction, and compactness from finite thresholds. Refutation attacks tested shift graphs, Mycielski constructions, high-girth high-chromatic graphs, and prescribed induced-tree avoidance; these reproduce the conjecture rather than refute it. Critics checked induced versus ordinary copies, finite-tree quantification, no-finite-coloring semantics, triangle definition, injectivity, universe scope, and adjacency biconditional.
Scope. Arbitrary-universe infinite vertex types; infinite chromatic means no proper coloring by any finite palette; all finite Mathlib trees; induced copies preserve adjacency and nonadjacency through an injective map.