Larrión–Neumann-Lara–Pizaña conjecture on clique divergence of non-negative Euler characteristic surfaces

Let $G$ be a locally cyclic graph of minimum degree $\delta\ge 4$ triangulating a closed surface of Euler characteristic $\chi\ge 0$; equivalently, the surface is a sphere, projective plane, torus or Klein bottle. A graph is clique divergent if its clique dynamics does not eventually cycle. Larrión–Neumann-Lara–Pizaña's conjecture. The graph $G$ is clique divergent. This conjecture asks whether every such triangulation has divergent clique dynamics; the paper presents it as an open question and attributes it to Larrión, Neumann-Lara and Pizaña.