Author

J. Löfberg

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Preprint Aug 2026

Second Order Zarankiewicz Number

We introduce the \emph{second order Zarankiewicz number} $z_2(m,n)$ for irreducible doubly simple biquadratic forms with $|E_1|=z(m,n)$, together with the intermediate recursive-line and signed parameters $z_{RL}(m,n)$ and $z_{SL}(m,n)$. They satisfy the unconditional hierarchy \[ \operatorname{BSR}(m,n) \ge z_2(m,n) \...

J. Löfberg, Li-Qun Qi · 7 citations · ⚡4

Preprint Sep 2026

Exact Second-Order Zarankiewicz Numbers for Complete-Graph Incidence Families

For $n\ge6$, $m=\binom n2$, let the complete-graph incidence family on $K_n$ have the vertices of $K_n$ as columns, its edges as rows, and the incidence graph as one-edge graph. The universal cell bound of L\"ofberg and Qi gives $z_2(m,n)\le Z(n):=\lfloor n(n-1)(n+2)/4\rfloor$. We implement the nested one-factorization...

Yan-Nan Chen, J. Löfberg, Li-Qun Qi · 2 citations · ⚡1