Problem #569: Let $k\geq 1$. What is the best possible $c_k$ such...

Let $k\geq 1$. What is the best possible $c_k$ such that\[R(C_{2k+1},H)\leq c_k m\]for any graph $H$ on $m$ edges without isolated vertices?

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Problem Statement

Let $k\geq 1$. What is the best possible $c_k$ such that\[R(C_{2k+1},H)\leq c_k m\]for any graph $H$ on $m$ edges without isolated vertices?

Categories: Graph Theory Ramsey Theory

See also the entry in the graphs problem collection.

Source: erdosproblems.com/569 | Last verified: January 15, 2026