Claims

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1978_01_01_gyarfas_lehel: Gyárfás and Lehel (1978) prove the tree packing conjecture when all but at most two of the trees are stars, and when every tree is a star or a path; a conference proceedings paper, so the claim is pending.

1983_09_01_fishburn: Fishburn (J. Graph Theory 7 (1983)) verifies the Gyárfás–Lehel tree packing conjecture for every n at most 9; accepted on the refereed publication, the result known from the paper's abstract and its citations.

1990_01_01_guichard_massman: Guichard and Massman (J. Combin. Math. Combin. Comput. 8 (1990)) verify by computer that the tree packing conjecture holds for n = 10 and n = 11, extending Fishburn's n at most 9; accepted on the journal publication.

2016_06_13_joos_kim_kuhn_osthus: Joos, Kim, Kühn and Osthus prove the tree packing conjecture for all large n whenever the trees beyond the first εn have bounded maximum degree; accepted on the refereed publication in J. Eur. Math. Soc. 21 (2019).

2021_06_22_allen_bottcher_clemens_hladky_piguet_taraz: An arXiv preprint of 2021 proves the tree packing conjecture for all large n when every tree has maximum degree at most cn/log n; it has no journal record, so the claim is pending.

2024_10_17_chalise_clark_gnang: An arXiv preprint of October 2024 claimed the tree packing conjecture for every n by a polynomial method; its authors withdrew it on 1 September 2026, citing an error in the proof of their Composition Lemma.

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