Israel Journal of Mathematics

, Volume 86, Issue 1–3, pp 397–407 | Cite as

A construction of 3-connected graphs

  • D. W. Barnette


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.


Bipartite Graph Complete Graph Multiple Edge Complete Bipartite Graph Recursive Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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.CrossRefGoogle Scholar
  2. [2]
    C. Thomassen,Planarity and duality of finite and infinite graphs, J. Comb. Theory, Ser. B29 (1980), 244–271.MATHMathSciNetGoogle Scholar
  3. [3]
    W. T. Tutte,A theory of 3-connected graphs, Indag. Math.23 (1961), 441–455.MathSciNetGoogle Scholar

Copyright information

© The Magnes Press 1994

Authors and Affiliations

  • D. W. Barnette
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

Personalised recommendations