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An approximate version of the Tree Packing Conjecture
- Source :
- Israel J. Math. 211 (2016), no. 1, 391-446
- Publication Year :
- 2014
-
Abstract
- 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 $\binom{n}{2}$ edges in total packs into $K_{(1+\epsilon)n}$. This implies asymptotic versions of the Tree Packing Conjecture of Gyarfas 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.<br />Comment: 38 pages, 2 figures; suggestions by an anonymous referee incorporated; accepted to Israel J Math
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Journal :
- Israel J. Math. 211 (2016), no. 1, 391-446
- Publication Type :
- Report
- Accession number :
- edsarx.1404.0697
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s11856-015-1277-2