Let $c > 0$ and let $f_{c} (n)$ be the maximal $m$ such that every graph $G$ with $n$ vertices and at least $c n^{2}$ edges, where each edge is contained in at least one triangle, must contain a book of size $m$ , that is, an edge shared by at least $m$ different triangles. Estimate $f_{c} (n)$ . In particular, is it true that $f_{c} (n) > n^{ϵ}$ for some $ϵ > 0$ ? Or $f_{c} (n) ≫ lo g n$ ?

Worked, still open.

graph theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

This is a well‑known Erdős–Rothschild problem. Most papers write your $f_c(n)$ as $h(n,c)$.

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

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

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