Networks

Minimum‐weight cycles in 3‐separable graphs

Journal Article

  • Author(s): Collette R. Coullard, L. Leslie Gardner, Donald K. Wagner
  • Article first published online: 07 Dec 1998
  • DOI: 10.1002/(SICI)1097-0037(199705)29:3<151::AID-NET3>3.0.CO;2-G
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Abstract

This paper presents a polynomial‐time algorithm for the minimum‐weight‐cycle problem on graphs that decompose via 3‐separations into well‐structured graphs. The problem is NP‐hard in general. Graphs that decompose via 3‐separations into well‐structured graphs include Halin, outer‐facial, delta‐wye, wye‐delta, flat, and twirl‐wheel graphs. For each of these classes of graphs, given the decomposition, the algorithm runs in linear time. © 1997 John Wiley & Sons, Inc. Networks 29: 151–160, 1997

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