Publication at Faculty of Mathematics and Physics |
2020
Abstract
Loebl, Komlos, and Sos conjectured that any graph with at least half of its vertices of degree at least k contains every tree with at most k edges. We propose a version of this conjecture for skew trees, i.e., we consider the class of trees with at most k edges such that the sizes of the colour classes of the trees have a given ratio.
We show that our conjecture is asymptotically correct for dense graphs. The proof relies on the regularity method.
Our result implies bounds on Ramsey number of several trees of given skew. (C) 2020 Elsevier Ltd. All rights reserved.