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.
Cite
@article{arxiv.1202.5003,
title = {A Planarity Test via Construction Sequences},
author = {Jens M. Schmidt},
journal= {arXiv preprint arXiv:1202.5003},
year = {2012}
}