On repetition thresholds of caterpillars and trees of bounded degree

Borut Lužar 1 Pascal Ochem 2 Alexandre Pinlou 2
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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. On repetition thresholds of caterpillars and trees of bounded degree. The Electronic Journal of Combinatorics, Open Journal Systems, 2018, 25 (1), pp.#P1.61. ⟨lirmm-01730276⟩

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