A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs

Halina Bielak

Discussiones Mathematicae Graph Theory (1999)

  • Volume: 19, Issue: 2, page 135-142
  • ISSN: 2083-5892

Abstract

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We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.

How to cite

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Halina Bielak. "A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs." Discussiones Mathematicae Graph Theory 19.2 (1999): 135-142. <http://eudml.org/doc/270371>.

@article{HalinaBielak1999,
abstract = {We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.},
author = {Halina Bielak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {planar graph; Ramsey number; complete graphs; planar Ramsey number},
language = {eng},
number = {2},
pages = {135-142},
title = {A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs},
url = {http://eudml.org/doc/270371},
volume = {19},
year = {1999},
}

TY - JOUR
AU - Halina Bielak
TI - A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1999
VL - 19
IS - 2
SP - 135
EP - 142
AB - We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.
LA - eng
KW - planar graph; Ramsey number; complete graphs; planar Ramsey number
UR - http://eudml.org/doc/270371
ER -

References

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  1. [1] H. Bielak, I. Gorgol, The Planar Ramsey Number for C₄ and K₅ is 13, to appear in Discrete Math. Zbl0995.05101
  2. [2] H. Bielak, Ramsey-Free Graphs of Order 17 for C₄ and K₆, submitted. 
  3. [3] J.A. Bondy, P. Erdős, Ramsey Numbers for Cycles in Graphs, J. Combin. Theory (B) 14 (1973) 46-54, doi: 10.1016/S0095-8956(73)80005-X. Zbl0248.05127
  4. [4] V. Chvátal, F. Harary, Generalized Ramsey Theory for Graphs, III. Small Off-Diagonal Numbers, Pacific J. Math. 41 (1972) 335-345. Zbl0227.05115
  5. [5] M. Clancy, Some Small Ramsey Numbers, J. Graph Theory 1 (1977) 89-91, doi: 10.1002/jgt.3190010117. Zbl0351.05121
  6. [6] P. Erdős, R.J. Faudree, C.C. Rousseau, R.H. Schelp, On Cycle-Complete Graph Ramsey Numbers, J. Graph Theory 2 (1978) 53-64, doi: 10.1002/jgt.3190020107. Zbl0383.05027
  7. [7] C.C. Rousseau, C.J. Jayawardene, The Ramsey number for a quadrilateral vs. a complete graph on six vertices, Congressus Numerantium 123 (1997) 97-108. Zbl0902.05050
  8. [8] R. Steinberg, C.A. Tovey, Planar Ramsey Number, J. Combin. Theory (B) 59 (1993) 288-296, doi: 10.1006/jctb.1993.1070. 
  9. [9] K. Walker, The Analog of Ramsey Numbers for Planar Graphs, Bull. London Math. Soc. 1 (1969) 187-190, doi: 10.1112/blms/1.2.187. Zbl0184.27705

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