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Journal Articles The Electronic Journal of Combinatorics Year : 2018

On repetition thresholds of caterpillars and trees of bounded degree

Pascal Ochem

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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Dates and versions

lirmm-01730276 , version 1 (20-12-2019)

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Borut Lužar, Pascal Ochem, Alexandre Pinlou. On repetition thresholds of caterpillars and trees of bounded degree. The Electronic Journal of Combinatorics, 2018, 25 (1), pp.#P1.61. ⟨10.37236/6793⟩. ⟨lirmm-01730276⟩
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