Repetition thresholds for subdivided graphs and trees

Pascal Ochem; Elise Vaslet

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et 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 - Informatique Théorique et Applications 46.1 (2012): 123-130. <http://eudml.org/doc/272998>.

@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 &gt; 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 - Informatique Théorique et Applications},
keywords = {combinatorics on words; repetition threshold; square-free coloring},
language = {eng},
number = {1},
pages = {123-130},
publisher = {EDP-Sciences},
title = {Repetition thresholds for subdivided graphs and trees},
url = {http://eudml.org/doc/272998},
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 - Informatique Théorique et Applications
PY - 2012
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 &gt; 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
UR - http://eudml.org/doc/272998
ER -

References

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  1. [1] A. Aberkane and J. Currie, There exist binary circular 5/2+ power free words of every length. Electron. J. Comb. 11 (2004) R10 Zbl1058.68084MR2035304
  2. [2] J. Chalopin and P. Ochem, Dejean’s conjecture and letter frequency. RAIRO-Theor. Inf. Appl. 42 (2008) 477–480. Zbl1147.68612MR2434030
  3. [3] F. Dejean, Sur un théorème de Thue. J. Combin. Theory. Ser. A13 (1972) 90–99. Zbl0245.20052MR300959
  4. [4] J. Grytczuk, Nonrepetitive colorings of graphs – a survey. Int. J. Math. Math. Sci. (2007), doi:10.1155/2007/74639 Zbl1139.05020MR2272338
  5. [5] P. Ochem, A generator of morphisms for infinite words. RAIRO-Theor. Inf. Appl. 40 (2006) 427–441. Zbl1110.68122MR2269202
  6. [6] A. Pezarski and M. Zmarz, Non-repetitive 3-Coloring of subdivided graphs. Electron. J. Comb. 16 (2009) N15 Zbl1165.05325MR2515755

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