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A construction of 3-connected graphs

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Abstract

We show that the 3-connected graphs can be generated from the complete graph on four vertices and the complete 3,3 bipartite graph by adding vertices and adding edges with endpoints on two edges meeting at a 3-valent vertex.

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References

  1. D.W. Barnette and B. Grünbaum,On Steinitz’s theorem concerning convex 3-polytopes and on some properties of planar graphs, inThe Many Facets of Graph Theory, Lecture Notes in Mathematics, Vol. 110, Springer, Berlin, 1969, pp. 27–39.

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  2. C. Thomassen,Planarity and duality of finite and infinite graphs, J. Comb. Theory, Ser. B29 (1980), 244–271.

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  3. W. T. Tutte,A theory of 3-connected graphs, Indag. Math.23 (1961), 441–455.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, CA, USA

    D. W. Barnette

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  1. D. W. Barnette
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Barnette, D.W. A construction of 3-connected graphs. Israel J. Math. 86, 397–407 (1994). https://doi.org/10.1007/BF02773688

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  • DOI: https://doi.org/10.1007/BF02773688

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