Repetition thresholds for subdivided graphs and trees

Pascal Ochem; Elise Vaslet

RAIRO - Theoretical Informatics and Applications (2012)

  • Volume: 46, Issue: 1, page 123-130
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Ochem, Pascal, and Vaslet, Elise. "Repetition thresholds for subdivided graphs and trees." RAIRO - Theoretical Informatics and Applications 46.1 (2012): 123-130. <http://eudml.org/doc/222007>.

@article{Ochem2012,
abstract = {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.},
author = {Ochem, Pascal, Vaslet, Elise},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Combinatorics on words; repetition threshold; square-free coloring; combinatorics on words},
language = {eng},
month = {3},
number = {1},
pages = {123-130},
publisher = {EDP Sciences},
title = {Repetition thresholds for subdivided graphs and trees},
url = {http://eudml.org/doc/222007},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Ochem, Pascal
AU - Vaslet, Elise
TI - Repetition thresholds for subdivided graphs and trees
JO - RAIRO - Theoretical Informatics and Applications
DA - 2012/3//
PB - EDP Sciences
VL - 46
IS - 1
SP - 123
EP - 130
AB - 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.
LA - eng
KW - Combinatorics on words; repetition threshold; square-free coloring; combinatorics on words
UR - http://eudml.org/doc/222007
ER -

References

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  1. A. Aberkane and J. Currie, There exist binary circular 5/2+ power free words of every length. Electron. J. Comb.11 (2004) R10 
  2. J. Chalopin and P. Ochem, Dejean’s conjecture and letter frequency. RAIRO-Theor. Inf. Appl.42 (2008) 477–480.  
  3. F. Dejean, Sur un théorème de Thue. J. Combin. Theory. Ser. A13 (1972) 90–99.  
  4. J. Grytczuk, Nonrepetitive colorings of graphs – a survey. Int. J. Math. Math. Sci. (2007), doi:10.1155/2007/74639  
  5. P. Ochem, A generator of morphisms for infinite words. RAIRO-Theor. Inf. Appl.40 (2006) 427–441.  
  6. A. Pezarski and M. Zmarz, Non-repetitive 3-Coloring of subdivided graphs. Electron. J. Comb.16 (2009) N15 

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