The smallest n such that every colouring of the edges of K n must contain a monochromatic star K 1,s+1 or a properly edge-coloured K t is denoted by f (s, t). Its existence is guaranteed by the Erdős–Rado Canonical Ramsey theorem and its value for large t was discussed by Alon, Jiang, Miller and Pritikin (Random Struct. Algorithms 23:409–433, 2003). In this note we primarily consider small values of t. We give the exact value of f (s, 3) for all s ≥ 1 and the exact value of f (2, 4), as well as reducing the known upper bounds for f (s, 4) and f (s, t) in general.
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机译：最小的n，使得K n 的每个边缘着色必须包含单色星K 1，s + 1 或适当边缘着色的K t < / sub>由f（s，t）表示。 Erdős-Rado规范Ramsey定理保证了它的存在，Alon，Jiang，Miller和Pritikin讨论了它的大t值（Random Struct。Algorithms 23：409-433，2003）。在本说明中，我们主要考虑t的较小值。我们给出所有s≥1的f（s，3）的精确值和f（2，4）的精确值，并减小f（s，4）和f（s，t的已知上限） ） 一般来说。
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