3 problems

Let $G$ be a cubic graph, meaning a $3$-regular finite simple graph, and let $\overline{G}$ denote its complement. A graph is Helly when its collection of cliques has the Helly pro…

Let $G$ be a finite simple graph, let $\overline{G}$ denote its complement, and call $G$ convergent when its iterated clique graphs contain only finitely many graphs up to isomorph…

Let $G$ be an $\alpha$-weakly-Helly graph, and let $G^{2\alpha}$ denote its $2\alpha$-th graph power. Power conjecture. The graph $G^{2\alpha}$ is Helly. This conjecture proposes t…