<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass{article}
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\begin{document}



\begin{align*}
X_{IN} &amp;= &amp; \textrm{ (sum of all edges with X on one end and a node inside the circle on the other end)} 
\\X_{OUT} &amp;= &amp; \textrm{ (sum of all edges with X on one end and a node outside the circle on the other end)}
\end{align*}




\begin{align*}
&amp;C(v_4,v_5,v_9)
\\&amp;= C(v_1,v_2,v_3,v_6,v_7,v_8)
\\&amp;= C(v_1,v_2,v_3) + C(v_6,v_7,v_8) - 2*c(v_1 v_2 v_3, v_6 v_7 v_8)
\\&amp;\leq  C(v_1,v_2,v_3) + C(v_6,v_7,v_8)
\\&amp;\leq  C(v_1,v_2,v_6) + C(v_6,v_7,v_8)
\end{align*}

\end{document}
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