ZoĆ© 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}