On ‐connected graphs
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Publication:5229537
DOI10.1002/JGT.22433zbMATH Open1417.05110arXiv1207.5357OpenAlexW2903198428MaRDI QIDQ5229537
Author name not available (Why is that?)
Publication date: 15 August 2019
Published in: (Search for Journal in Brave)
Abstract: A graph G is called (2k, k)-connected if G is 2k-edge-connected and G-v is k-edge-connected for every vertex v. The study of (2k, k)-connected graphs is motivated by a conjecture of Frank which states that a graph has a 2-vertex-connected orientation if and only if it is (4, 2)-connected. In this paper, we provide a construction of the family of (2k, k)-connected graphs for k even which generalizes the construction given by Jord'an for k = 2. We also solve the corresponding connectivity augmentation problem: given a graph G and an integer k geq 2, what is the minimum number of edges to be added to make G (2k, k)-connected. Both these results are based on a new splitting-off theorem for (2k, k)-connected graphs.
Full work available at URL: https://arxiv.org/abs/1207.5357
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