An Anti-Ramsey Theorem on Cycles
β Scribed by J.J. Montellano-Ballesteros; V. Neumann-Lara
- Publisher
- Springer Japan
- Year
- 2005
- Tongue
- English
- Weight
- 152 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0911-0119
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## Abstract We determine the maximum number of colors in a coloring of the edges of __K~m,n~__ such that every cycle of length 2__k__ contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs. For positive integers __q__
We present a very simple proof of the fact (due to P. Erd~s and R. Rado) that Ram~ey's theorem doesn't hold for partitions of infinite subsets. We also present a proof of an induced Ramsey theorem for partitions of complete subgraphs (due to W. Deuber and authors) based on the theorem of R. Graham a