The Ramsey number r(C₇,C₇,C₇)

Ralph Faudree; Annette Schelten; Ingo Schiermeyer

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 1, page 141-158
  • ISSN: 2083-5892

Abstract

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Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.

How to cite

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Ralph Faudree, Annette Schelten, and Ingo Schiermeyer. "The Ramsey number r(C₇,C₇,C₇)." Discussiones Mathematicae Graph Theory 23.1 (2003): 141-158. <http://eudml.org/doc/270210>.

@article{RalphFaudree2003,
abstract = {Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.},
author = {Ralph Faudree, Annette Schelten, Ingo Schiermeyer},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Ramsey numbers; extremal graphs; multicolor Ramsey numbers; cycles},
language = {eng},
number = {1},
pages = {141-158},
title = {The Ramsey number r(C₇,C₇,C₇)},
url = {http://eudml.org/doc/270210},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Ralph Faudree
AU - Annette Schelten
AU - Ingo Schiermeyer
TI - The Ramsey number r(C₇,C₇,C₇)
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 1
SP - 141
EP - 158
AB - Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.
LA - eng
KW - Ramsey numbers; extremal graphs; multicolor Ramsey numbers; cycles
UR - http://eudml.org/doc/270210
ER -

References

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  1. [1] A. Bialostocki and J. Schönheim, On Some Turan and Ramsey Numbers for C₄, Graph Theory and Combinatorics, Academic Press, London, (1984) 29-33. Zbl0554.05036
  2. [2] J.A. Bondy and P. Erdős, Ramsey Numbers for Cycles in Graphs, J. Combin. Theory (B) 14 (1973) 46-54. Zbl0248.05127
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  10. [10] T. Łuczak, R(Cₙ,Cₙ,Cₙ) ≤ (4+o(1))n, J. Combin. Theory (B) 75 (1999) 174-187. 
  11. [11] S.P. Radziszowski, Small Ramsey Numbers, Electronic J. Combin. 1 (1994) update 2001. 
  12. [12] A. Schelten, Bestimmung von Ramsey-Zahlen zweier und dreier Graphen (Dissertation, TU Bergakademie Freiberg, 2000). 
  13. [13] P. Rowlinson amd Yang Yuangsheng, On the Third Ramsey Numbers of Graphs with Five Edges, J. Combin. Math. and Combin. Comp. 11 (1992) 213-222. Zbl0756.05078
  14. [14] P. Rowlinson and Yang Yuangsheng, On Graphs without 6-Cycles and Related Ramsey Numbers, Utilitas Mathematica 44 (1993) 192-196. Zbl0789.05070

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