Strict Confluent Drawing

TL;DR

This paper introduces strict confluent drawing, a crossing-free graph visualization method with unique path constraints, proves its computational complexity, and identifies efficient algorithms for specific cases.

Contribution

It formally defines strict confluent drawing, proves NP-completeness for general graphs, and provides polynomial algorithms for outerplanar cases with fixed vertex order.

Findings

Determining strict confluent drawings is NP-complete.

Outerplanar strict confluent drawings with fixed vertex order can be decided in polynomial time.

The concept enhances graph visualization with unique path constraints.

Abstract

We define strict confluent drawing, a form of confluent drawing in which the existence of an edge is indicated by the presence of a smooth path through a system of arcs and junctions (without crossings), and in which such a path, if it exists, must be unique. We prove that it is NP-complete to determine whether a given graph has a strict confluent drawing but polynomial to determine whether it has an outerplanar strict confluent drawing with a fixed vertex ordering (a drawing within a disk, with the vertices placed in a given order on the boundary).