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Seven largest trees pack

Cisiński Maciej, Żak Andrzej

Opuscula Mathematica

2024

Vol. 44, no. 5

673--688

The Tree Packing Conjecture (TPC) by Gyárfás states that any set of trees T2, . . . , Tn−1, Tn such that Ti has i vertices pack into Kn. The conjecture is true for bounded degree trees, but in general, it is widely open. Bollobás proposed a weakening of TPC which states that k largest trees pack. The latter is true if none tree is a star, but in general, it is known only for k = 5. In this paper we prove, among other results, that seven largest trees pack.