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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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 464, 2017, pp. 95–111.
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Pastor, A.V. On Critical 3-Connected Graphs with Two Vertices of Degree 3. Part I. J Math Sci 236, 532–541 (2019). https://doi.org/10.1007/s10958-018-4131-3
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DOI: https://doi.org/10.1007/s10958-018-4131-3