Induced trees in triangle-free graphs

Details Induced trees in triangle-free graphs Induced trees in triangle-free graphs

2007-11-30

arxiv.org/abs/0711.4829v1

Mathematics

Combinatorics

Scientific paper

We prove that every connected triangle-free graph on $n$ vertices contains an
induced tree on $\exp(c\sqrt{\log n})$ vertices, where $c$ is a positive
constant. The best known upper bound is $(2+o(1))\sqrt n$. This partially
answers questions of Erdos, Saks, and Sos and of Pultr.

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