There are two relevant questions:

(1) We know an edge set $C$ is a rigid cycle in $\mathcal{G}_2(n)$ if and only if $|E(C)|=2|V(C)|−2$ and $|F|≤2|V(F)|−3$ for every proper subset $F$ of $E(C)$. Thus, I want to know: Is a rigid cycle a chordal graph? (It can be found in Wiki that chordal graphs are also called as "rigid circuit graphs". But i can't find the connection between it and rigid cycle. Are they the same thing?)

(2) A graph $G=(V,E)$ is defined as pseudocycle iff $|E|=2|V|−2$ and $F\leq 2|V(F)|−2$, $ \forall \ \emptyset\subset F\subset E$. Thus, I also would like to know: Is a pseudocycle a chordal graph?

Thanks very much!