Ringel-type conjecture for degenerate graphs

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Fix an integer DD. Degenerate-graph Ringel-type conjecture. There exists n0∈Nn_0\in\mathbb{N} such that, for every n≥n0n\ge n_0, if GG is a DD-degenerate graph on nn vertices with m≥n−1m\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.

References

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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