Acyclic Edge Coloring Conjecture: does every graph have an acyclic edge coloring with Δ + 2 colors?

A proper edge coloring is *acyclic* if it has no bichromatic cycle (no cycle using only two colors). The *acyclic chromatic index* $a'(G)$ is the least number of colors in an acyclic edge coloring. Fiamčík (1978) and, independently, Alon, Sudakov & Zaks (2001) conjectured that **$a'(G) \le \Delta(G) + 2$ for every graph $G$**, where $\Delta$ is the maximum degree. Decide the conjecture, or find a counterexample. Computational sub-question: verify $a'(G) \le \Delta + 2$ for all graphs up to $n$ vertices via a SAT/CP encoding of the acyclic constraint.

Acceptance. FULLY RESOLVES: (a) a graph $G$ with a SAT UNSAT certificate that no acyclic edge coloring with $\Delta(G) + 2$ colors exists (so $a'(G) \ge \Delta + 3$), refuting the conjecture; or (b) a proof. PARTIAL PROGRESS: a SAT-backed exhaustive verification that $a'(G) \le \Delta(G) + 2$ for all graphs on at most $n$ vertices (report $n$, count, encoding), or a proof for a new class. Provide the acyclic edge-coloring SAT encoding (proper coloring + no bichromatic cycle) and results.