An approximate version of the Tree Packing Conjecture

0454288 - MÚ 2017 RIV IL eng J - Journal Article
Böttcher, J. - Hladký, Jan - Piguet, Diana - Taraz, A.
An approximate version of the Tree Packing Conjecture.
Israel Journal of Mathematics. Roč. 211, č. 1 (2016), s. 391-446. ISSN 0021-2172. E-ISSN 1565-8511
Institutional support: RVO:67985840 ; RVO:67985807
Keywords : Ringel's conjecture * Gyarfas-Lehel conjecture * Tree packing
Subject RIV: BA - General Mathematics
Impact factor: 0.796, year: 2016
http://link.springer.com/article/10.1007%2Fs11856-015-1277-2

We prove that for any pair of constants $\epsilon > 0$ and $\Delta$ and for $n$ sufficiently large, every family of trees of orders at most $n$, maximum degrees at most $\Delta$, and with at most $(2^n)$ edges in total packs into $K_{(1+\epsilon)n} . This implies asymptotic versions of the Tree Packing Conjecture of Gyárfás 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.
Permanent Link: http://hdl.handle.net/11104/0255006