deletions | additions       diff --git a/section_Unanimity_and_2_colorability__.tex b/section_Unanimity_and_2_colorability__.tex  index 73cdeef..da0ddcd 100644  --- a/section_Unanimity_and_2_colorability__.tex  +++ b/section_Unanimity_and_2_colorability__.tex 
...
We give a sufficient condition for non-convergence of UP:  \begin{lemma}  Let $G$ be a (serial but non necessarily functional) an  influence profile and $\O$ be an opinion profile, such that, for some $p\in \Atoms $, for all $i,j\in\N$: if $i\in R_p(j)$, then $O_i_{p}\neq O_j{p}$. Then the UP does not converge. \end{lemma}  Recall that a graph is properly two-colored if no node has a successor of the same color. The above result can be reformulated as follows: if for some $p\in\Atoms$, $\O$ properly colors $G_p$, then $\O$ does not converge. In fact, it is easy to see that in such a case, all agents will change their opinion on $p$ at every step, entering an oscillation of size $2$. Note that this limit case of opinion distribution is yet another special case of DeGroot processes, another example within the intersection between the two frameworks of propositional opinion diffusion and DeGroot.