An approximate version of the tree packing conjecture

Böttcher, Julia ORCID: 0000-0002-4104-3635, 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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Abstract

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
Official URL:	http://www.springer.com/mathematics/journal/11856
Additional Information:	© 2016 Springer
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	04 Feb 2016 16:51
Last Modified:	24 Oct 2024 07:27
Projects:	EP/J501414/1
Funders:	Engineering and Physical Sciences Research Council, London Mathematical Society, University of Warwick
URI:	http://eprints.lse.ac.uk/id/eprint/65240

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