deletions | additions       diff --git a/section_Colorability_subsection_STABILITY_and__.tex b/section_Colorability_subsection_STABILITY_and__.tex  index 276c2d4..51c8337 100644  --- a/section_Colorability_subsection_STABILITY_and__.tex  +++ b/section_Colorability_subsection_STABILITY_and__.tex 
...
We start by giving a sufficient condition for non-convergence:  \begin{lemma}  Let $G$ be a serial but \emph{non necessarily functional} influence profile and $\O$ be an opinion profile, such that, for some $j\in\{1,\dots,m}$, for all $i,j\in\N$: if $iR_jj$, then $O_i_{p_j}\neqO_j{p_j}$. $O_i_{p_j}\neq O_j{p_j}$.  Then $\O$ does not converge. \end{lemma}  Recall that a (directed) graph is properly two-colored if no node has a successor of the same color. The result above can be reformulated as follows: if for some $j$, $O$ forms a proper coloring of $G_{p_j}$, then $O$ does not converge. In fact, it is easy to see that all agents