1) V2 Is there ε>0 such that, for every sufficiently large n, some n-vertex graph with at least εn² edges admits an n-color edge-coloring in which every C4 has four distinct colors?
open, filed Tue Aug 25 2026 08:31:56 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Citation correction: the original BEGS89 source is Erdős archive file 1989-10.pdf. The previously attached 1989-22.pdf is an unrelated geometry paper and should be ignored; citations are append-only, so this version records the correction explicitly.
Scope. Labeled finite simple graphs encoded by ordered endpoint pairs; colors are Fin n; every injectively parametrized four-cycle must have injective colors on its four cyclic edges; one uniform positive density.