Schematic Representation of Large Biconnected Graphs

Suppose that a biconnected graph is given, consisting of large component plus several other smaller components, each separated from the main by separation pair. We investigate existence and computation time schematic representations structure such where drawn as disk, vertices take part in pairs are points on boundary small components placed outside disk represented non-intersecting lunes connecting their pairs. consider drawing conventions for representations, according to different ways account size components. map problem testing one suitably constrained $1$-page book-embeddings propose polynomial-time algorithms.