2023/08/30 by Sabine Cornelsen, Cornelsen, Sabine, Gregor Diatzko +1
Computer Science · #Advanced Graph Theory Research #Computational Geometry (cs.CG) #Constraint Satisfaction and Optimization #Data Structures and Algorithms (cs.DS) #Data Visualization and Analytics #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.2308.16020
openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and to determine their nesting structure. A linear-time algorithm for this problem was already proposed by Kant. However, using common graph data structures, we found the subroutine dealing with triangulated graphs difficult to implement in such a way that it actually runs in linear time. As a drop-in replacement, we provide a different, easy-to-implement linear-time algorithm that decomposes a triangulated graph into its 4-connected components and computes the respective nesting structure. The algorithm is based on depth-first search.