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Consider a balanced bipartite graph $G=(U,V,E)$, i.e., a bipartite graph with $|U|=|V|$. An independent set $I$ of $G$ is balanced if $|I \cap U| = |I \cap V|$. The bipartite independence number of $...

Let $G(A,B)$ be a bipartite graph with $|A| = |B| = n$, where $n$ is sufficiently large(thus, $o(n)/n,o(n^2)/n^2\ll 1$). The edge density of $G$ is $d = \frac{e(A,B)}{n^2}$, where $e(A,B)$ denotes the ...

Given real $\pm1$ matrix $M\in\Bbb R^{n\times m}$ we have that cut-norm is given by $$\|M\|_C=\max_{\mathcal I\subseteq[n],\mathcal J\subseteq[m]}\Big|\sum_{(i,j)\in\mathcal I\times\mathcal J}M_{ij}\...