Towards Characterizing Strict Outerconfluent Graphs

摘要

Confluent drawings of graphs are geometric representations in the plane, in which vertices are mapped to points, but edges are not drawn as individually distinguishable geometric objects. Instead, an edge is represented by the presence of a smooth curve between two vertices in a system of arcs and junctions. More formally, a confluent drawing D of a graph G = (V,E) consists of a set of points representing the vertices, a set of junction points, and a set of smooth arcs, such that each arc starts and ends at a vertex point or a junction, no two arcs intersect (except at common endpoints), and all arcs meeting in a junction share the same tangent line in the junction point. There is an edge (u, v) ∈ E if and only if there is a smooth path from u to v in D that does not pass through any other vertex.