Maintaining the 3-edge-connected components of a graph on-line
SIAM Journal on Computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the number of small cuts in a graph
Information Processing Letters
Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Computing All Small Cuts in Undirected Networks
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
How to Draw the Minimum Cuts of a Planar Graph (Extended Abstract)
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
The 3-Edge-Components and a Structural Description of All 3-Edge-Cuts in a Graph
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
A representation of cuts within 6/5 times the edge connectivity with applications
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edgecuts 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.