video.ias.edu/csdm/2016/0229-Babai

video.ias.edu/csdm/2016/0301-Babai

@Jim Nice question. One might try to make fewer typos (or call the irrelevant inconsistencies if you prefer), but the question is clear. (I would color the vertices in each $H_k$ by a unique color, to ensure that the automorphism group is a subgroup of the direct product beyond doubt.) My guess is that there is actually a counterexample for $x=3$, i.e. that the global automorphism $\sigma$ is not the product of two automorphisms $\alpha_1, \alpha_2$ with $\alpha_k \in Aut(M_{(k,k+1)}$.

However, I am currently very busy. And it will be quite some time (=months) before I even addressed to most recent "backlog" (from working with the first serious pilot customer of a new product). So please don't interpret my silence as negative judgment of your progress. I just know that I have too many open tasks to cope with, and well, those tasks are more important to me than my interactions with you or vzn.

We are working with finite set, so we can't afford to repeat.