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• 09:11, 4 June 2024 Roundgod talk contribs created page 组合数学 (Spring 2024)/Problem Set 4 (Created page with "== Problem 1 == Recall that the smallest number <math>R(k,\ell)</math> satisfying the condition in the Ramsey theory is called the '''Ramsey number'''. Prove that: * <math>R(4,3)\leq 9</math>. (Hint: Proof by contradiction. Color the edges of <math>K_9</math> in red and blue, and assume that there are no red triangles and no blue <math>4</math>-cliques. Try to determine the number of red and blue edges adjacent to each vertex.) * <math>R(4,4)\leq 18</math>. ==Problem 2...")