Abstract
For a k-connected graph G, we introduce the notion of a block and construct a block tree. This construction generalizes, for \(k \geqslant 1\), the known constructions for blocks of a connected graph. We apply the introduced notions to describe the set of vertices of a k-connected graph G such that the graph remains k-connected after deleting these vertices. We discuss some problems related to simultaneous deleting of vertices of a k-connected graph without loss of k-connectivity. Bibliography: 5 titles.
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Karpov, D.V., Pastor, A.V. On the Structure of a k-Connected Graph. Journal of Mathematical Sciences 113, 584–597 (2003). https://doi.org/10.1023/A:1021146226285
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DOI: https://doi.org/10.1023/A:1021146226285