Email this article On Critical 3-Connected Graphs with Two Vertices of Degree 3. Part I
- Authors: Pastor A.V.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics and Peter the Great St. Petersburg Polytechnic University
- Issue: Vol 236, No 5 (2019)
- Pages: 532-541
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242262
- DOI: https://doi.org/10.1007/s10958-018-4131-3
- ID: 242262
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Abstract
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.
About the authors
A. V. Pastor
St. Petersburg Department of Steklov Institute of Mathematics and Peter the Great St. Petersburg Polytechnic University
Author for correspondence.
Email: pastor@pdmi.ras.ru
Russian Federation, St. Petersburg
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