Cookies?
Library Header Image
LSE Research Online LSE Library Services

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

[img]
Preview
PDF - Accepted Version
Download (779kB) | Preview
Identification Number: 10.1007/s11856-015-1277-2

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
Sets: Departments > Mathematics
Date Deposited: 04 Feb 2016 16:51
Last Modified: 20 Oct 2019 02:21
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

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics