A Planarity Test via Construction Sequences

Details A Planarity Test via Construction Sequences A Planarity Test via Construction Sequences

2012-02-22

arxiv.org/abs/1202.5003v1

Computer Science

Data Structures and Algorithms

Scientific paper

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.

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