Graphs with convex balls

In this paper, we investigate the graphs in which all balls are convex and groups acting on them geometrically (which call CB-graphs CB-groups). These have been introduced characterized by Soltan Chepoi (1983) Farber Jamison (1987). CB-groups generalize systolic (alias bridged) weakly groups, play an important role geometric group theory. We present metric local-to-global characterizations of CB-graphs. Namely, characterize $G$ as whose triangle-pentagonal complexes $X(G)$ simply connected radius at most $3$ convex. Similarly to graphs, prove a dismantlability result for $G$: show that their squares $G^2$ dismantlable. This implies Rips contractible. Finally, adapt extend approach Januszkiewicz Swiatkowski (2006) Chalopin et al. (2020) Helly biautomatic.