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

Discussiones Mathematicae Graph Theory (1999)

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

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topHalina 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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- [2] H. Bielak, Ramsey-Free Graphs of Order 17 for C₄ and K₆, submitted.
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- [8] R. Steinberg, C.A. Tovey, Planar Ramsey Number, J. Combin. Theory (B) 59 (1993) 288-296, doi: 10.1006/jctb.1993.1070.
- [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