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An approximate version of the tree packing conjecture

Böttcher, Julia, Hladký, Jan, Piguet, Diana and Taraz, Anusch (2016) An approximate version of the tree packing conjecture. Israel Journal of Mathematics, 211 (1). pp. 391-446. ISSN 0021-2172

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Identification Number: 10.1007/s11856-015-1277-2


We prove that for any pair of constants ε > 0 and ∆ and for n sufficiently large, every family of trees of orders at most n, maximum degrees at most ∆, and with at most (n2) edges in total packs into K(1+ε)n. This implies asymptotic versions of the Tree Packing Conjecture of Gy´arf´as from 1976 and a tree packing conjecture of Ringel from 1963 for trees with bounded maximum degree. A novel random tree embedding process combined with the nibble method forms the core of the proof.

Item Type: Article
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Additional Information: © 2016 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 04 Feb 2016 16:51
Last Modified: 20 Apr 2021 01:06
Projects: EP/J501414/1
Funders: Engineering and Physical Sciences Research Council, London Mathematical Society, University of Warwick

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