Repetition thresholds for subdivided graphs and trees
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 123-130.

The repetition threshold introduced by Dejean and Brandenburg is the smallest real number α such that there exists an infinite word over a k-letter alphabet that avoids β-powers for all β > α. We extend this notion to colored graphs and obtain the value of the repetition thresholds of trees and “large enough” subdivisions of graphs for every alphabet size.

DOI: 10.1051/ita/2011122
Classification: 68R15
Keywords: combinatorics on words, repetition threshold, square-free coloring
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Ochem, Pascal; Vaslet, Elise. Repetition thresholds for subdivided graphs and trees. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 123-130. doi : 10.1051/ita/2011122. http://www.numdam.org/articles/10.1051/ita/2011122/

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