Listing All Plane Graphs

(Extended Abstract)
  • Katsuhisa Yamanaka
  • Shin-ichi Nakano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4921)


In this paper we give a simple algorithm to generate all connected rooted plane graphs with at most m edges. A “rooted” plane graph is a plane graph with one designated (directed) edge on the outer face. The algorithm uses O(m) space and generates such graphs in O(1) time per graph on average without duplications. The algorithm does not output the entire graph but the difference from the previous graph. By modifying the algorithm we can generate all connected (non-rooted) plane graphs with at most m edges in O(m 3) time per graph.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Katsuhisa Yamanaka
    • 1
  • Shin-ichi Nakano
    • 1
  1. 1.Department of Computer ScienceGunma UniversityGunmaJapan

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