RAIRO-Theor. Inf. Appl.
Volume 46, Number 1, January-March 2012Special issue dedicated to the 13th "Journées Montoises d'Informatique Théorique"
|Page(s)||123 - 130|
|Published online||07 October 2011|
Repetition thresholds for subdivided graphs and trees
CNRS, LRI, Université Paris-Sud 11, 91405
2 IML, UMR 6206, Université Aix-Marseille II, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France
Received: 2 November 2010
Accepted: 5 August 2011
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.
Mathematics Subject Classification: 68R15
Key words: Combinatorics on words / repetition threshold / square-free coloring
© EDP Sciences 2011
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