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Ramsey Problems with Bounded Degree Spread

Published online by Cambridge University Press:  12 September 2008

G. Chen  and
R. H. Schelp
G. Chen
Affiliation:
North Dakota State University, Fargo, ND 58105
R. H. Schelp
Affiliation:
Memphis State University, Memphis, TN 38152
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Abstract

Let k be a positive integer, k ≥ 2. In this paper we study bipartite graphs G such that, for n sufficiently large, each two-coloring of the edges of the complete graph Kn gives a monochromatic copy of G, with some k of its vertices having the maximum degree of these k vertices minus the minimum degree of these k vertices (in the colored Kn) at most k − 2.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 3 , September 1993 , pp. 263 - 269
Copyright
Copyright © Cambridge University Press 1993

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References

[1]Albertson, M. O. (preprint) People who know people.Google Scholar
[2]Albertson, M. O. and Berman, D. M. (preprint) Ramsey graphs without repeated degrees.Google Scholar
[3]Erdős, P., Chen, G., Rousseau, C. C. and Schelp, R. H. (1993) Ramsey problems involving degrees in edge-colored complete graphs of vertices belonging to monochromatic subgraphs. Europ. J. Combinatorics 14 183–189.CrossRefGoogle Scholar
[4]Graham, R. L., Rothschild, B. R. and Spencer, J. H. (1990) Ramsey Theory (2nd Edition), John Wiley & Sons, New York.Google Scholar
[5]Kővári, T., Sós, V. T. and Túran, P. (1954) On a problem of Zarankiewicz. Colloq. Math. 3 50–57.CrossRefGoogle Scholar