Tree packing conjecture for families of trees

Let nNn\in\mathbb{N}, and let (Ts)s[n](T_s)_{s\in[n]} be a family of trees such that v(Ts)=sv(T_s)=s for every s[n]s\in[n]. Tree packing conjecture. The family (Ts)s[n](T_s)_{s\in[n]} packs into the complete graph KnK_n. The paper presents this as one of the central tree-packing conjectures and later proves it for sufficiently large nn when the trees have maximum degree O(n/logn)O(n/\log n); the general case with large-degree vertices remains open.

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Primary source

Peter Allen, Julia Böttcher, Dennis Clemens, Jan Hladký, Diana Piguet and Anusch Taraz, “The tree packing conjecture for trees of almost linear maximum degree”, arXiv:2106.11720 (2022).

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