Planarity of the 2-level cactus model

Sabine Cornelsen, Yefim Dinitz, Dorothea Wagner

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The 2-level cactus introduced by Dinitz and Nutov in [5] 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.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings
EditorsAndreas Brandstadt, Van Bang Le
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540427074, 9783540427070
StatePublished - 1 Jan 2001
Event27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001 - Boltenhagen, Germany
Duration: 14 Jun 200116 Jun 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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