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An approximate version of the Tree Packing Conjecture
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SYSNO ASEP 0454288 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title An approximate version of the Tree Packing Conjecture Author(s) Böttcher, J. (GB)
Hladký, Jan (MU-W) RID, SAI, ORCID
Piguet, Diana (UIVT-O) RID, ORCID, SAI
Taraz, A. (DE)Source Title Israel Journal of Mathematics. - : Magnes press - ISSN 0021-2172
Roč. 211, č. 1 (2016), s. 391-446Number of pages 56 s. Language eng - English Country IL - Israel Keywords Ringel's conjecture ; Gyarfas-Lehel conjecture ; Tree packing Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 ; UIVT-O - RVO:67985807 UT WOS 000377265200017 EID SCOPUS 84953281806 DOI 10.1007/s11856-015-1277-2 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2017
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