Given i, j positive integers, let K denote a bipartite complete graph and let i, j ## Ž . R m, n be the smallest integer a such that for any r-coloring of the edges of K r a, a one can always find a monochromatic subgraph isomorphic to K . In other m, n Ž . Ä 4 words, if a G R m, n then every mat
On Ramsey graphs without bipartite subgraphs
✍ Scribed by Jaroslav Nešetřil; Vojtěch Rödl
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 388 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
NeSetfil, J. and V. Riidl, On Ramsey graphs without bipartite subgraphs, Discrete Mathematics 101 (1992) 223-229.
We prove that for every graph H without triangles and K,,,,,m, n G 2, there exists a Ramsey graph with the same properties.
This answers a problem due to Erd& and Faudree. Moreover we characterize all (edge-) Ramsey classes Forb(K,,,).
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