<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*}
&amp;C(v_1) + C(v_2) + C(v_5) + C(v_6)
\\&amp;\geq C(v_1) + C(v_2) + C(v_5) + C(v_6) - 2*c(v_1, v_2)
\\&amp;= C(v_1,v_2) + C(v_5) + C(v_6)
\\&amp;\geq C(v_1,v_2) + C(v_5) + C(v_6) - 2*c(v_1 v_2, v_6)
\\&amp;= C(v_1,v_2, v_6) + C(v_5)
\\&amp;\geq C(v_1,v_2, v_3) + C(v_5)  &amp; \textrm{ if $v_6$ is connected to $v_1$ or $v_2$}
\\&amp;\geq  C(v_1,v_2, v_3) + C(v_5) - 2*c(v_1 v_2 v_3, v_5)
\\&amp;=  C(v_1,v_2, v_3, v_5)
\\&amp;\geq  C(v_1,v_2, v_3, v_4)   &amp; \textrm{ if $v_5$ is connected to $v_1$ or $v_2$ or $v_3$}
\end{align*}

\end{document}
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