On Finding the K Best Cuts in a Network. Hamacher, H. W., Picard, J.C, & Queyranne, M. Operations Research Letters, 2(6):303--305, March, 1984.
On Finding the K Best Cuts in a Network [link]Paper  doi  abstract   bibtex   
We show that the O(K · n4) algorithm of Hamacher (1982) for finding the K best cut-sets fails because it may produce cuts rather than cut-sets. With the convention that two cuts and are different whenever X ≠ Y the K best cut problem can be solved in O(K · n4).
@article{ Hamacher1984a,
  abstract = {We show that the O(K · n4) algorithm of Hamacher (1982) for finding the K best cut-sets fails because it may produce cuts rather than cut-sets. With the convention that two cuts and are different whenever X ≠ Y the K best cut problem can be solved in O(K · n4).},
  author = {Hamacher, Horst W. and Picard, Jean-Claude and Queyranne, Maurice},
  doi = {10.1016/0167-6377(84)90083-X},
  file = {:Users/KunihiroWASA/Dropbox/paper/1984/Hamacher, Picard, Queyranne, On Finding the K Best Cuts in a Network, 1984.pdf:pdf},
  issn = {01676377},
  journal = {Operations Research Letters},
  keywords = {Flow algorithm,cut,ranking of solutions},
  month = {March},
  number = {6},
  pages = {303--305},
  title = {{On Finding the K Best Cuts in a Network}},
  url = {http://www.sciencedirect.com/science/article/pii/016763778490083X http://linkinghub.elsevier.com/retrieve/pii/016763778490083X},
  volume = {2},
  year = {1984}
}

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