Loebl-Komlós-Sós Conjecture: dense case
Abstrakt
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 $G$.