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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 273.05111

**Autor: ** Burr, Stefan A.; Erdös, Paul; Spencer, J.H.

**Title: ** Ramsey theorems for multiple copies of graphs. (In English)

**Source: ** Trans. Am. Math. Soc. 209, 87-99 (1975).

**Review: ** If G and H are graphs, define the ``Ramsey number'' r(G,H) to be the least number p such that if the edges of the complete graph K_{p} are colored red and blue (say), either the red graph contains G as a subgraph or the blue graph contains H. Let mG denote the union of m disjoint copies of G. The following result is proved: Let G and H have k and l points respectively and have point independence numbers of i and j respectively. Then N-1 \leq r(mG,nH) \leq N+C, where N = km+ln- **max** (mi,nj) and where C is an effectively computable function of G and H. The method used permits exact evaluation of r(mG,nH) for various choices of G and H, especially when m = n or G = H. In particular, r(mK_{3},nK_{3}) = 3m+2n when m \geq n, m \geq 2.

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C15 Chromatic theory of graphs and maps

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