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arXiv · 1702.01058

On repetition thresholds of caterpillars and trees of bounded degree

Borut Lužar·Pascal Ochem·Alexandre Pinlou
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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.

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Borut Lužar, Pascal Ochem, Alexandre Pinlou. 2017-02-03. On repetition thresholds of caterpillars and trees of bounded degree. https://arxiv.org/abs/1702.01058

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