Induced Trees in Triangle-Free Graphs - Matoušek, Jiří; Šámal, Robert (The Electronic Journal of Combinatorics, 2008)
We prove that every connected triangle-free graph on n vertices contains an induced tree on (cn ) vertices, where c is a positive constant. The best known upper bound is (2+o(1))n. This partially answers questions of Erdős, Saks, and Sós and of Pultr.