6 problems

Reduced clique graph recognition conjecture. There is a polynomial-time algorithm for deciding whether a given graph is isomorphic to $C_R(G)$ for some chordal graph $G$.

Chordal graph representation conjecture. Let $H$ be a chordal graph. There are chordal graphs $G$ and $G'$ such that $H$ is isomorphic to both $C(G)$ and $C_R(G')$.

Seven-hole conjecture. There is no chordal graph $G$ such that $C_R(G)$ contains an induced cycle with seven or more vertices.

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 a finite simple graph. Its clique graph is the intersection graph of the cliques of $G$, and define the iterated clique graphs by … … for $n\geq 1$. The sequence is call…

Let $G$ be a graph, and let $K(G)$ denote its clique graph. Define $K^{0}(G)=G$ and $K^{n}(G)=K(K^{n-1}(G))$ for $n\geq 1$. A graph is K-homotopy permanent when $K^{n}(G)\simeq G$…