eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-09-04
490
499
10.4230/LIPIcs.APPROX-RANDOM.2014.490
article
An Approximate Version of the Tree Packing Conjecture via Random Embeddings
Böttcher, Julia
Hladký, Jan
Piguet, Diana
Taraz, Anusch
We prove that for any pair of constants a>0 and D and for n sufficiently large, every family of trees of orders at most n, maximum degrees at most D, and with at most n(n-1)/2 edges in total packs into the complete graph of order (1+a)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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol028-approx-random2014/LIPIcs.APPROX-RANDOM.2014.490/LIPIcs.APPROX-RANDOM.2014.490.pdf
tree packing conjecture
Ringel’s conjecture
random walks
quasirandom graphs