A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs
Halina Bielak
Discussiones Mathematicae Graph Theory, Tome 19 (1999), p. 135-142 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:270371 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1090,
     author = {Halina Bielak},
     title = {A note on the Ramsey number and the planar Ramsey number for C4 and complete graphs},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {19},
     year = {1999},
     pages = {135-142},
     zbl = {0958.05093},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1090}
}

Halina Bielak. A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs. Discussiones Mathematicae Graph Theory, Tome 19 (1999) pp. 135-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1090/

[000] [1] H. Bielak, I. Gorgol, The Planar Ramsey Number for C₄ and K₅ is 13, to appear in Discrete Math. | Zbl 0995.05101

[001] [2] H. Bielak, Ramsey-Free Graphs of Order 17 for C₄ and K₆, submitted.

[002] [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. | Zbl 0248.05127

[003] [4] V. Chvátal, F. Harary, Generalized Ramsey Theory for Graphs, III. Small Off-Diagonal Numbers, Pacific J. Math. 41 (1972) 335-345. | Zbl 0227.05115

[004] [5] M. Clancy, Some Small Ramsey Numbers, J. Graph Theory 1 (1977) 89-91, doi: 10.1002/jgt.3190010117. | Zbl 0351.05121

[005] [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. | Zbl 0383.05027

[006] [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. | Zbl 0902.05050

[007] [8] R. Steinberg, C.A. Tovey, Planar Ramsey Number, J. Combin. Theory (B) 59 (1993) 288-296, doi: 10.1006/jctb.1993.1070.

[008] [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. | Zbl 0184.27705