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Efficient Planarity Testing

Authors:

John Hopcroft and

Robert TarjanAuthors Info & Claims

Journal of the ACM (JACM), Volume 21, Issue 4

Pages 549 - 568

https://doi.org/10.1145/321850.321852

Published: 01 October 1974 Publication History

Abstract

This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm used depth-first search and has O(V) time and space bounds, where V is the number of vertices in G. An ALGOL implementation of the algorithm succesfully tested graphs with as many as 900 vertices in less than 12 seconds.

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https://doi.org/10.1016/j.ejc.2023.103815
Nakano S(2024)(t, s)-Completely Independent Spanning TreesWALCOM: Algorithms and Computation10.1007/978-981-97-0566-5_26(365-376)Online publication date: 18-Mar-2024
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Index Terms

Efficient Planarity Testing
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 21, Issue 4

Oct. 1974

172 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321850

Issue’s Table of Contents

Copyright © 1974 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1974

Published in JACM Volume 21, Issue 4

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Tarjan RZwick U(2024)Finding strong components using depth-first searchEuropean Journal of Combinatorics10.1016/j.ejc.2023.103815119(103815)Online publication date: Jun-2024
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