A Planarity Test via Construction Sequences

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 conceptually simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. This implies a linear-time planarity test. Our approach is radically different from all previous linear-time planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise.