Ringel-type conjecture for degenerate graphs

Fix an integer DD. Degenerate-graph Ringel-type conjecture. There exists n0Nn_0\in\mathbb{N} such that, for every nn0n\ge n_0, if GG is a DD-degenerate graph on nn vertices with mn1m\ge n-1 edges, then 2m+12m+1 copies of GG pack into K2m+1K_{2m+1}. The paper presents this as a possible analogue of Ringel's conjecture for degenerate graphs, but gives no resolution.

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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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