seems good

main.tex

@@ -115,6 +115,30 @@ Authors of \cite{vygen_fptas_2024} $\subset$ authors  of
 How to derive normalized min cut for connectivity interdiction?
 
 
+\begin{equation*}
+\begin{aligned}
+\max&   &                   z&          &   & \\
+s.t.&   &   \sum_{e} y_e c(e) &\leq B   &   &\text{(budget for $F$)}\\
+&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ forms a cut)}\\
+&       &   \sum_{e} \min(0,x_e-y_e) w(e)&\geq z   &   &\\
+&       &   y_e,x_e&\in\{0,1\}      &   &\forall e
+\end{aligned}
+\end{equation*}
+
+we can assume that $y_e\leq x_e$.
+
+\begin{equation*}
+\begin{aligned}
+\min&   &                   \sum_{e} (x_e&-y_e) w(e)          &   & \\
+% s.t.&   &   \sum_{e} (x_e-y_e) w(e)&\geq z   &   &\\
+s.t.&       &   \sum_{e\in T} x_e&\geq 1   &   &\forall T\quad \text{($x$ forms a cut)}\\
+&       &   \sum_{e} y_e c(e) &\leq B   &   &\text{(budget for $F$)}\\
+&       &   x_e&\geq y_e   &   &\forall e\quad(F\subset C)\\
+&       &   y_e,x_e&\in\{0,1\}      &   &\forall e
+\end{aligned}
+\end{equation*}
+
+Now this LP looks similar to the normalized min-cut problem.
 
 \section{Random Stuff}