Planarity of the 2-level Cactus Model

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2001
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Dinitz, Yefim
Wagner, Dorothea
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The 2-level cactus introduced by Dinitz and Nutov (1995) is a data structure that represents the minimum and minimum+1 edge-cuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used e.g. in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.

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ISO 690CORNELSEN, Sabine, Yefim DINITZ, Dorothea WAGNER, 2001. Planarity of the 2-level Cactus Model
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@unpublished{Cornelsen2001Plana-6111,
  year={2001},
  title={Planarity of the 2-level Cactus Model},
  author={Cornelsen, Sabine and Dinitz, Yefim and Wagner, Dorothea}
}
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