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Ramsey Problems with Bounded Degree Spread

  • G. Chen (a1) and R. H. Schelp (a2)
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.

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References
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[1]Albertson, M. O. (preprint) People who know people.
[2]Albertson, M. O. and Berman, D. M. (preprint) Ramsey graphs without repeated degrees.
[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 183189.
[4]Graham, R. L., Rothschild, B. R. and Spencer, J. H. (1990) Ramsey Theory (2nd Edition), John Wiley & Sons, New York.
[5]Kővári, T., Sós, V. T. and Túran, P. (1954) On a problem of Zarankiewicz. Colloq. Math. 3 5057.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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