no. 1
Repetition thresholds for subdivided graphs and trees
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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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     title = {Repetition thresholds for subdivided graphs and trees},
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     pages = {123--130},
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Ochem, Pascal; Vaslet, Elise. Repetition thresholds for subdivided graphs and trees. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 123-130. doi: 10.1051/ita/2011122

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