Let $G$ be a graph of genus $g$ embedded on a surface of genus $g$. Let $s,t \in V(G)$. Consider a minimal $s,t$-cut $C$ in $G$. Let $H$ consist of the union of faces adjacent to $E(C)$. Notice that $H$ is also embedded on a surface. Is the dual $H^*$ of $H$ always $2$-connected?

Any pointer, reference or proof will be appreciated.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.