23 papers
Exact and Asymptotic Values for Weak Limited Augmented Zarankiewicz Numbers in the Case
Liqun Qi, Yannan Chen, Johan Löfberg
We determine the exact weak limited augmented Zarankiewicz numbers for all : \[ z_{wL}(m,3)= \begin{cases} m+3+\left\lceil \dfrac{m}{2}\right\rceil+1, & 9\le…
A Weak Condition for Limited Augmented Zarankiewicz Numbers
Liqun Qi, Chunfeng Cui, Yi Xu
The authors define a weaker version of the limited augmented Zarankiewicz number by replacing the opposite‑cell condition with an acyclic dependency rule and a simplified local pro…
Three-Edges and the SOS Rank of Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We extend the augmented bipartite graph framework for biquadratic sum-of-squares (SOS) ranks by introducing -edges -- triples of cells representing squares of three-term bilinea…
A General Lower Bound for the Limited Augmented Zarankiewicz Number based upon Complete Graphs
Liqun Qi, Chunfeng Cui, Yi Xu
The limited augmented Zarankiewicz number satisfies , where is the maximum SOS rank of $m\times…
Biquadratic SOS Rank and Augmented Zarankiewicz Number
Liqun Qi, Chunfeng Cui, Yi Xu
This paper introduces the concepts of the augmented Zarankiewicz number and the limited augmented Zarankiewicz number , which are natural combinatorial extensi…
Narrowing the Gap: SOS Ranks of Biquadratic Forms and a Lower Bound of
Yi Xu, Chunfeng Cui, Liqun Qi
We investigate the maximum sum-of-squares (SOS) rank of biquadratic forms in the critical case of variables, where the general bounds are currently $7 \leq \mathrm{BSR…