4 citations · 5 across the 26 of their papers we have counts for
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The Second-Order Augmented Zarankiewicz Number
Liqun Qi, Chunfeng Cui
The second-order Zarankiewicz number and the biquadratic sum-of-squares rank are related by the unconditional hierarchy \[ \mathrm{BSR}(m,n)\ \ge\ z_…
A Weak Condition for Limited Augmented Zarankiewicz Numbers
Liqun Qi, Chunfeng Cui, Yi Xu
This paper introduces the weak augmented Zarankiewicz number and the weak limited augmented Zarankiewicz number , which are combinatorial extensions of t…
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…
Sum of Squares Rank of Biquadratic Forms and The Zarankiewicz Number
Chunfeng Cui, Liqun Qi, Yi Xu
Denote the maximum sos rank of sum of squares (SOS) biquadratic forms by . In this paper, we show that and conjecture that $BSR(m, n…
Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definitenes…