Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Claim. For and , every family of trees with packs into . This is the computer verification of David R. Guichard and John D. Massman, A note on packing complete graphs with trees, J. Combin. Math. Combin. Comput. 8 (1990), 123--126 (no DOI; the volume carries a year and no month, so this page is dated to 1990 with a nominal day). The note generates Fishburn's universally recursive families and by computer and shows directly that the one exceptional tree in each case still packs, "proving the Gyárfás--Lehel conjecture for " and "for " (p. 124); its abstract adds that an approach suggested by Fishburn is unlikely to work in general. The corpus holds the publisher's copy on its card and pages the verification at verification_p124. The note is not a site key; a thread comment of 27 August 2026 named it.
Covers. The instances of Problem 743 with and , every family of trees included; for them the answer is yes. With Fishburn's verification for , every is settled, and is the first order no published exhaustive check covers.
Depends on. Fishburn's verification: the note follows Fishburn's route, splitting into his half-complete graphs and (p. 124); for the odd-order trees pack into by Fishburn's , and the families and are generated by computer from his hand-made and (pp. 124--125); the note's own computation packs the even-order trees into and the odd-order trees into .
Acceptance. Refereed: the Journal of Combinatorial Mathematics and
Combinatorial Computing, volume 8 (zbMATH record read). The
site's commentary does not name the note, and the site labels the problem
FALSIFIABLE, an open problem, so no reviewed evidence exists. The
computation itself has not been repeated, and no independent review is
supplied.