Decomposing Triangulations into 4-Connected Components
Abstract
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.
Cite
@article{arxiv.2308.16020,
title = {Decomposing Triangulations into 4-Connected Components},
author = {Sabine Cornelsen and Gregor Diatzko},
journal= {arXiv preprint arXiv:2308.16020},
year = {2023}
}