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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Abstract

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:	https://www.springer.com/journal/11856
Additional Information:	© 2021 Springer Nature Switzerland AG
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	11 May 2021 10:48
Last Modified:	12 Dec 2024 02:31
URI:	http://eprints.lse.ac.uk/id/eprint/110429

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