Strengthened Ringel packing conjecture for bounded tree orders

Let nn be a positive integer. Consider any family of trees in which every individual tree has order at most n+1n+1 and the total number of edges is at most (2n+12)\binom{2n+1}{2}. Strengthened Ringel packing conjecture. The family packs into K2n+1K_{2n+1}. This strengthens Ringel's conjecture by allowing a family of trees of possibly different orders while retaining the relevant order and edge bounds. The source labels this as a proposed strengthening; the supplied status evidence reports an asymptotic result only for a related bounded-maximum-degree conjecture, not a full proof.

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Primary source

Julia Böttcher, Jan Hladký, Diana Piguet and Anusch Taraz, “An approximate version of the Tree Packing Conjecture”, arXiv:1404.0697 (2014).

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