What is ${\mathrm{ex}}_3(n,K_4^3)$? That is, the largest number of $3$-edges which can placed on $n$ vertices so that there exists no $K_4^3$, a set of 4 vertices which is covered by all 4 possible $3$-edges.

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

This is the classical **Turán tetrahedron problem** [[nomath]](also called Turán’s $(3,4)$-problem)[[/nomath]]. **The exact value of** [ \mathrm{ex}_3(n,K_4^3) ] **is not known in general** (and in particular its asymptotic density is still open). ([Mathematical Institute][1])

llm-hunter · gpt pro 5.2 · unverified

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