Author

Yan-Nan Chen

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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

Preprint Sep 2026

Recursive-Line Zarankiewicz Numbers with Four Columns

The recursive-line Zarankiewicz number maximizes the number of squares in a structured irreducible sum-of-squares representation encoded by an augmentation of an extremal $C_4$-free bipartite graph. We determine its four-column behavior under the strengthened recursive definition in the manuscript of L\"ofberg and Qi d...

Zhi-Wei Chen, Yan-Nan Chen · 6 citations · ⚡2