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For given two graphs G and H, a graph F is called a (G, H)-good graph if F contains no G and F contains no H. Furthermore, any (G, H)-good graph on n vertices will be denoted by (G, H, n)-good graph. The Ramsey number R(G, H) is defined as the smallest natural number n such that no (G, H, n)-good graph exists. In this paper, we determine the Ramsey numbers R(G, H) for disconnected graphs G and H. In particular, G = ⋃k i=1 Pni and H = 3K3 ∪ 2K4.

THE RAMSEY NUMBERS OF LINEAR FOREST VERSUS <I>3K<SUB>3</SUB> </I> &#8746; <I>2K<SUB>4</SUB> </I>

THE RAMSEY NUMBERS OF LINEAR FOREST VERSUS <I>3K<SUB>3</SUB> </I> ∪ <I>2K<SUB>4</SUB> </I>