Embedding trees in graphs with independence number two.

Let G be a graph of order n and k an integer not great than n. Erdős and Sós conjectured that if G has at least n ( k − 2 ) / 2 edges, then G contains all trees of order k. Loebl, Komlós and Sós conjectured that if at least n / 2 vertices of G have degree at least k − 1 , then G contains all trees of order k. In this paper, it is shown that both the conjectures are true for graphs with independence number two, and our results generalize some known results. [ABSTRACT FROM AUTHOR]