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ZoƩ Christoff edited section_Colorability_and_unanimity_In__.tex
about 8 years ago
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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
$j\in\{1,\dots,m\}$, $G_pj$ $p\in\Atoms$, $G_p$ is not $2$-colorable, or
\item[] There is a
$j\in\{1,\dots,m\}$, $p\in\Atoms$, such that: for all $i,j\in\N$ if $j\in
R_j(i)$, $O_i{p_j}\neq O_j(p_j)$. R_p(i)$, $O_i{p}\neq O_j(p)$.
\end{itemize}
\end{theorem}