Gyeong-Won Jeong

A New Upper Bound for the Turán Density of the Tetrahedron

We prove that the Tur\'an density of the tetrahedron $K_4^{(3)}$ satisfies $\pi(K_4^{(3)}) \le 14993367693127837/26880000000000000<0.557789$, improving Baber's upper bound of $0.5615$ and closing about $62\%$ of the gap to the conjectured value $5/9$. The proof uses an exact seven-vertex flag-algebra certificate incorp...