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The double star S (m 1, m 2) is obtained from joining the centres of a star with m 1 leaves
and a star with m 2≤ m 1 leaves. We give a short proof of a new upper bound on the two …

A conjecture of Loebl, also known as the $(n/2-n/2-n/2) $ Conjecture, states that if $ G $ is an
$ n $-vertex graph in which at least $ n/2$ of the vertices have degree at least $ n/2$, then …

In a series of four papers we prove the following relaxation of the Loebl--Komlós--Sós
conjecture: For every α>0 there exists a number k_0 such that for every k>k_0, every n …

We prove a version of the Loebl–Komlós–Sós Conjecture for dense graphs. For each q> 0
there exists a number n 0∈ N such that for each n> n 0 and k> qn the following holds: if G is …

Loebl, Komlós, and Sós conjectured that if at least half of the vertices of a graph G have
degree at least some k∈ N, then every tree with at most k edges is a subgraph of G. Our …

Loebl, Koml\'os and S\'os conjectured that every $ n $-vertex graph $ G $ with at least $ n/2$
vertices of degree at least $ k $ contains each tree $ T $ of order $ k+ 1$ as a subgraph. We …

Let TsH be the graph obtained from a given graph H by subdividing each edge s times.
Motivated by a problem raised by Igor Pak [Mixing time and long paths in graphs, in Proc. of …

We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded
maximum degree. In particular we determine asymptotically the two and three color Ramsey …

This thesis is concerned with embedding problems for large graphs under various types of
degree conditions in the host graph. A conjecture by Bollobás and Komlós states that every …