Geodesic
On repetition thresholds of caterpillars and trees of bounded degree
Borut Lužar1 ; Pascal Ochem2 ; Alexandre Pinlou2
1Faculty of Information Studies, Novo mesto, Slovenia. Pavol J. Safarik University, Faculty of Science, Kosice, Slovakia.
2LIRMM, Université de Montpellier, CNRS, Montpellier, France.
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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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.
DOI : 10.37236/6793
Classification : 68R15, 05C15
Mots-clés : infinite word, repetition threshold, graph coloring

Borut Lužar  1   ; Pascal Ochem  2   ; Alexandre Pinlou  2

1 Faculty of Information Studies, Novo mesto, Slovenia. Pavol J. Safarik University, Faculty of Science, Kosice, Slovakia.
2 LIRMM, Université de Montpellier, CNRS, Montpellier, France. 
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     journal = {The electronic journal of combinatorics},
     year = {2018},
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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, Tome 25 (2018) no. 1. doi: 10.37236/6793

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