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

0486590 - ÚI 2018 US eng V - Research Report
Klimošová, T. - Piguet, Diana - Rozhoň, Václav
A version of the Loebl-Komlós-Sós conjecture for skewed trees.
Cornell University, 2018. 28 s. arXiv.org e-Print archive, arXiv:1802.00679 [math.CO].
R&D Projects: GA ČR GJ16-07822Y; GA ČR GBP202/12/G061
Institutional support: RVO:67985807
Keywords : extremal graph theory * tree embedding * Loebl-Komlos-Sos conjecture * regularity lemma
Subject RIV: BA - General Mathematics
https://arxiv.org/abs/1802.00679

Loebl, Komlós, and Sós 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 number of several trees of given skew.
Permanent Link: http://hdl.handle.net/11104/0281354