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.
Complete list of metadatas

Contributor : Alexandre Pinlou <>
Submitted on : Tuesday, March 13, 2018 - 10:47:46 AM
Last modification on : Monday, August 5, 2019 - 3:26:03 PM

Links full text




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⟩



Record views