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On repetition thresholds of caterpillars and trees of bounded degree (1702.01058v1)
Published 3 Feb 2017 in cs.DM and math.CO
Abstract: 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.