On Repetition Thresholds of Caterpillars and Trees of Bounded Degree

  • Borut Lužar
  • Pascal Ochem
  • Alexandre Pinlou
Keywords: Infinite word, Repetition threshold, Graph coloring


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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