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On the structure of
vertex cuts separating the ends of a graph
Gareth R. Wilkes |
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Vol. 278 (2015), No. 2, 479–510
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Abstract |
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Dinic, Karzanov and Lomonosov showed that the minimal edge cuts of a finite graph have the structure of a cactus, a tree-like graph constructed from cycles. Evangelidou and Papasoglu extended this to minimal cuts separating the ends of an infinite graph. In this paper we show that minimal vertex cuts separating the ends of a graph can be encoded by a succulent, a mild generalisation of a cactus that is still tree-like. We go on to show that the earlier cactus results follow from our work. |
Keywords
ends, cuts, cactus, succulent
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Mathematical Subject Classification 2010
Primary: 05C40
Secondary: 20E08, 57M07
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Milestones
Received: 9 October 2014
Revised: 30 January 2015
Accepted: 20 April 2015
Published: 6 October 2015
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Authors |
| Gareth R. Wilkes | |
| Mathematical Institute University of Oxford Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG United Kingdom |
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