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Claim. If $T_2,\ldots,T_n$ are trees with $|T_k|=k$ and all but at most two of them are stars, or every one of them is a star or a path, then $K_n$ is the edge-disjoint union of copies of the $T_k$. These are the results of A. Gyárfás and J. Lehel, Packing trees of different order into $K_n$, Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Colloq. Math. Soc. János Bolyai 18, North-Holland (1978), 463--469, as [GuMa90] and [ABCHPT21] cite it, the paper in which the conjecture itself was stated; the volume carries a year and no month, so this page is dated to 1978 with a nominal day. The paper is not held, and its results are second-hand: the site's commentary states both cases; Janzer and Montgomery ([JaMo24] p. 1) state both; Bollobás ([Bo83] p. 203, a refereed note) attests the case in which all but at most two trees are stars.

Covers. The instances of Problem 743, for every $n$, in which all but at most two of the trees are stars, and those in which every tree is a star or a path; for them the answer is yes. Every other family is not covered.

Depends on. Nothing in this wiki.

Standing. Claimed: the paper is a conference proceedings paper, and no evidence that the volume was refereed is held, so it is not refereed under the rules of this corpus. The attestations by Bollobás and by Janzer and Montgomery, and the site's credit in the commentary of a problem the site labels FALSIFIABLE, are context and not acceptance evidence.