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# Loebl-Komlós-Sós Conjecture: dense case

1. 1.
0451115 - MÚ 2017 RIV US eng J - Journal Article
Loebl-Komlós-Sós Conjecture: dense case.
Journal of Combinatorial Theory. B. Roč. 116, January (2016), s. 123-190. ISSN 0095-8956. E-ISSN 1096-0902
R&D Projects: GA MŠk(CZ) 1M0545
Institutional support: RVO:67985840 ; RVO:67985807
Keywords : Loebl-Komlós-Sós Conjecture * Ramsey number of trees
Subject RIV: BA - General Mathematics
Impact factor: 0.829, year: 2016
http://www.sciencedirect.com/science/article/pii/S009589561500088X

We prove a version of the Loebl-Komlos-Sos Conjecture for dense graphs. For each $q>0$ there exists a number $n_0 \in \mathbb N$ such that for each $n>n_0$ and $k>qn$ the following holds: if $G$ is a graph of order $n$ with at least $\frac{n}{2}$ vertices of degree at least $k$, then each tree of order $k+1$ is a subgraph of $G$.