On repetition thresholds of caterpillars and trees of bounded degree (Q1753030)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On repetition thresholds of caterpillars and trees of bounded degree |
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On repetition thresholds of caterpillars and trees of bounded degree (English)
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25 May 2018
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Summary: The \textit{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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infinite word
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repetition threshold
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graph coloring
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