  The repetition threshold is the smallest real number $\alpha$ such that there
exists an infinite word over a $k$-letter alphabet that avoids repetition of
exponent strictly greater than $\alpha$. This notion can be generalized to
graph classes. In this paper, we completely determine the repetition thresholds
for caterpillars and caterpillars of maximum degree $3$. Additionally, we
present bounds for the repetition thresholds of trees with bounded maximum
degrees.
