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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.490
URN: urn:nbn:de:0030-drops-47184
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4718/
Böttcher, Julia ; Hladký, Jan ; Piguet, Diana ; Taraz, Anusch
An Approximate Version of the Tree Packing Conjecture via Random Embeddings
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Abstract
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.
BibTeX - Entry
@InProceedings{bttcher_et_al:LIPIcs:2014:4718,
author = {Julia B{\"o}ttcher and Jan Hladk{\'y} and Diana Piguet and Anusch Taraz},
title = {{An Approximate Version of the Tree Packing Conjecture via Random Embeddings}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
pages = {490--499},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-74-3},
ISSN = {1868-8969},
year = {2014},
volume = {28},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4718},
URN = {urn:nbn:de:0030-drops-47184},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.490},
annote = {Keywords: tree packing conjecture, Ringel’s conjecture, random walks, quasirandom graphs}
}
| Keywords: | tree packing conjecture, Ringel’s conjecture, random walks, quasirandom graphs | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) | |
| Issue date: | 2014 | |
| Date of publication: | 04.09.2014 |
