On the vertex-face graphs of triangulations
On the vertex-face graphs of triangulations
Let $G=(V(G),E(G))$ be a triangulation with vertex set $V(G)=\{v_1,v_2, \ldots,v_n\}$ and edge set $E(G)$ embedded on an orientable surface with genus $g$. Define $G^{\nabla}$ to be the graph obtained from $G$ by inserting a new vertex $v_{\phi}$ to each face $\phi$ of $G$ and adding three new edges $(u,v_{\phi}),(v,v_{\phi})$ and …