A version of the Loebl-Komlós-Sós conjecture for skew trees

@article{Klimovsova2020AVO,
  title={A version of the Loebl-Koml{\'o}s-S{\'o}s conjecture for skew trees},
  author={Tereza Klimovsov'a and D. Piguet and V{\'a}clav Rozhoň},
  journal={Eur. J. Comb.},
  year={2020},
  volume={88},
  pages={103106}
}
Loebl, Koml\'os, and S\'os 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 skewed 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… Expand
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