Canonical cactus representation for minimum cuts


DOI: 10.1007/BF03167227

Cite this article as:
Nagamochi, H. & Kameda, T. Japan J. Indust. Appl. Math. (1994) 11: 343. doi:10.1007/BF03167227


It is known that all minimum cuts in a networkN can be embedded in a cactus whose size is bounded by a linear function of the number of vertices inN, such that any minimum cut ofN can be easily obtained as a minimum cut of the cactus. However, such a representation for a given network is not unique. We introduce two canonical forms of cactus representation for the minimum cuts and show their uniqueness. These cacti contain at most twice as many vertices asN.

Key words

undirected multigraph cactus representation minimum cut canonical form isomorphism 

Copyright information

© JJIAM Publishing Committee 1994

Authors and Affiliations

  1. 1.Department of Applied Mathematics and PhysicsKyoto UniversityKyotoJapan
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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