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Journal of Mathematical Sciences

, Volume 236, Issue 5, pp 532–541 | Cite as

On Critical 3-Connected Graphs with Two Vertices of Degree 3. Part I

  • A. V. Pastor
Article
  • 8 Downloads

A 3-connected graph G is said to be critical if for any vertex υ ∈ V (G) the graph G − υ is not 3-connected. Entringer and Slater proved that any critical 3-connected graph contains at least two vertices of degree 3. In this paper, a classification of critical 3-connected graphs with two vertices of degree 3 is given in the case where these vertices are adjacent. The case of nonadjacent vertices of degree 3 will be studied in the second part of the paper, which will be published later.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of Mathematics and Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia

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