The cycle set of a graph $G$ on $n$ vertices is a set $A\subseteq \{3,\dots ,n\}$ such that there is a cycle in $G$ of length $\ell$ if and only if $\ell \in A$. Let $f(n)$ count the number of possible such $A$. Prove that $f(n)=o(2^n)$.Prove that $f(n)/2^{n/2}\to \infty$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let $f(n)$ be the number of sets (A\subseteq{3,\dots,n}) that occur as the **cycle set** of some graph on $n$ vertices.

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.