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Claim. For every $n\le9$ and every family of trees $T_2,\ldots,T_n$ with $|T_k|=k$, the complete graph $K_n$ is the edge-disjoint union of copies of the $T_k$. This is the closing result of P. C. Fishburn, Packing graphs with odd and even trees, J. Graph Theory 7 (1983), no. 3, 369--383, doi:10.1002/jgt.3190070309 (the issue is dated September 1983 in the Crossref record, the month in this page's name with a nominal day). The paper is not held. Its abstract (Crossref record read) examines two conjectures that jointly imply the Gyárfás--Lehel conjecture and ends "The conjectures are also valid for all trees when $n\le9$, so that the Gyárfás-Lehel conjecture holds for $n\le9$"; Janzer and Montgomery ([JaMo24] p. 1) and Guichard and Massman ([GuMa90] pp. 123--124) cite it for this verification. The site's commentary credits the $n\le9$ case to Fishburn under the key [Fi83], which names his other 1983 paper, on degree-sequence packing; the problem page records that the key is wrong and the result is this paper's.

Covers. The instances of Problem 743 with $n\le9$, every family of trees included; for them the answer is yes. Every $n\ge10$ is not covered by this page.

Depends on. Nothing in this wiki.

Acceptance. Refereed: the Journal of Graph Theory, volume 7, issue 3 (Crossref record read). As context and not as evidence, the site's curator, Thomas Bloom, credits Fishburn with the $n\le9$ case in the problem's commentary; the site labels the problem FALSIFIABLE, an open problem, so the credit settles nothing and is no reviewed evidence. The result is recorded from the paper's abstract and from the citations named above, and no proof review is supplied.