English

A Planarity Test via Construction Sequences

Data Structures and Algorithms 2012-02-23 v1 Discrete Mathematics

Abstract

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise.

Keywords

Cite

@article{arxiv.1202.5003,
  title  = {A Planarity Test via Construction Sequences},
  author = {Jens M. Schmidt},
  journal= {arXiv preprint arXiv:1202.5003},
  year   = {2012}
}
R2 v1 2026-06-21T20:23:37.613Z