Generating all planar 0-,1-,2-,3-connected graphs

  • Peter Läuchli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)


A graph grammar is given which generates all k- connected planar graphs for given k=0,1,2,3; n=# of vertices, m=# of edges, and (for k=0) p=# of components. The method is based on two elementary operations, namely (1) Joining two nonadjacent vertices by an edge, and (2) Replacing a vertex by two adjacent vertices. The operations are applied to plane embeddings, in such a way that the result is again a plane graph. All essentially different embeddings are generated.


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    Montanari, U.G.; Separable graphs, planar graphs and web grammars. Information and control 16 (1970) 243–267.Google Scholar
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    Tinhofer, G.; Zufallsgraphen, Carl Hanser Verlag, München 1980.Google Scholar
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    Tutte, W.T.; A theory of 3-connected graphs, Indag. Math. 23 (1961) 441–455.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Peter Läuchli
    • 1
  1. 1.Institut für Informatik ETH-ZentrumZürich

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