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Computer Science > Data Structures and Algorithms

arXiv:1202.5003 (cs)
[Submitted on 22 Feb 2012]

Title:A Planarity Test via Construction Sequences

Authors:Jens M. Schmidt
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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.
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM)
Cite as: arXiv:1202.5003 [cs.DS]
  (or arXiv:1202.5003v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1202.5003

Submission history

From: Jens M. Schmidt [view email]
[v1] Wed, 22 Feb 2012 18:46:56 UTC (140 KB)
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