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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.
@article{ITA_2012__46_1_123_0,
author = {Ochem, Pascal and Vaslet, Elise},
title = {Repetition thresholds for subdivided graphs and trees},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {123--130},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2011122},
mrnumber = {2904965},
zbl = {1247.68211},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011122/}
}
TY - JOUR AU - Ochem, Pascal AU - Vaslet, Elise TI - Repetition thresholds for subdivided graphs and trees JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 123 EP - 130 VL - 46 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011122/ DO - 10.1051/ita/2011122 LA - en ID - ITA_2012__46_1_123_0 ER -
%0 Journal Article %A Ochem, Pascal %A Vaslet, Elise %T Repetition thresholds for subdivided graphs and trees %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 123-130 %V 46 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011122/ %R 10.1051/ita/2011122 %G en %F ITA_2012__46_1_123_0
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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