On Critical 3-Connected Graphs with Two Vertices of Degree 3. Part I
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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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- 3.D. V. Karpov, “The decomposition tree of a biconnected graph,” Zap. Nauchn. Semin. POMI, 417, 86–105 (2013).Google Scholar
- 4.D. V. Karpov, “The tree of cuts and minimal k-connected graphs,” Zap. Nauchn. Semin. POMI, 427, 22–40 (2014).Google Scholar
- 6.D. V. Karpov and A. V. Pastor, “The structure of decomposition of a triconnected graph,” Zap. Nauchn. Semin. POMI, 391, 90–148 (2011).Google Scholar
- 7.A. V. Pastor, “On a decomposition of a 3-connected graph into cyclically 4-edge-connected components,” Zap. Nauchn. Semin. POMI, 450, 109–150 (2016).Google Scholar
- 13.W. T. Tutte, Connectivity in Graphs, Toronto Univ. Press, Toronto (1966).Google Scholar