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Perfectly packing graphs with bounded degeneracy and many leaves

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Clemens, Dennis and Taraz, Anusch (2022) Perfectly packing graphs with bounded degeneracy and many leaves. Israel Journal of Mathematics. ISSN 0021-2172

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Identification Number: 10.1007/s11856-022-2447-7


We prove that one can perfectly pack degenerate graphs into complete or dense n-vertex quasirandom graphs, provided that all the degenerate graphs have maximum degree(Formula Presented.)., and in addition Ω(n) of them have at most (1 − Ω(1))n vertices and Ω(n) leaves. This proves Ringel’s conjecture and the Gyárfás Tree Packing Conjecture for all but an exponentially small fraction of trees (or sequences of trees, respectively).

Item Type: Article
Official URL:
Additional Information: © 2021 Springer Nature Switzerland AG
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 11 May 2021 10:48
Last Modified: 10 Jan 2023 10:00

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