deletions | additions       diff --git a/section_Colorability_and_unanimity_In__.tex b/section_Colorability_and_unanimity_In__.tex  index 259920c..23d8e96 100644  --- a/section_Colorability_and_unanimity_In__.tex  +++ b/section_Colorability_and_unanimity_In__.tex 
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Let $\G=(G_{p_1},\dots,G_{p_m})$ be a symmetric (and non-necessarily functional) influence profile and $\O=(O_1,\dots,O_n)$ be an opinion profile.  The UP converges for $\O$ on $\G$ iff:  \begin{itemize}  \item[] For all $j\in\{1,\ldots,m\}$, $j\in\{1,\dots,m\}$,  $G_pj$ is not $2$-colorable, or \item[] There is a $j\in\{1,\ldots,m\}$, $j\in\{1,\dots,m\}$,  such that $\O$ properly colors $G_pj$: for all $i,j\in\$ such that $i\in R_j(j)$, $O{p_i}\neq O{p_j}$. $j\in R_j(i)$, $O_i{p_j}\neq O_j(p_j)$.  \end{itemize}  \end{proposition}  \begin{proof}  \dots  \end{proof}  \subsection{modal logic and colorability}