A Characterization of DFS Cotree Critical Graphs

  • Hubert de Fraysseix
  • Patrice Ossona de Mendez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)


We give a characterization of DFS-cotree critical graphs which is central to the linear time Kuratowski finding algorithm implemented in PIGALE1.


  1. 1.
    H. de Fraysseix and P. Ossona de Mendez, An algorithm to find Kuratowski subdivision in DFS cotree critical graphs, Proceedings of the twelfth australasian workshop on combinatorial algorithms (Edy Try Baskoro, ed.), Institut Teknologi Bandung, Indonesia, 2001.Google Scholar
  2. 2.
    H. de Fraysseix and P. Rosenstiehl, A discriminatory theorem of Kuratowski subgraphs, Lecture Notes in Mathematics 1018 (1981), 214–222.Google Scholar
  3. 3.
    -, A characterization of planar graphs by Trémaux orders, Combinatorica 5 (1985), no. 2, 127–135.Google Scholar
  4. 4.
    J.E Hopcroft and R.E. Tarjan, Efficient planarity testing, J. Assoc. Comput. Math. 21 (1974), 549–568.MATHMathSciNetGoogle Scholar
  5. 5.
    K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271–293.MATHGoogle Scholar
  6. 6.
    W.T. Tutte, Graph theory, Encyclopedia of Mathematics and its applications, vol. 21, Addison-Wesley, 1984.Google Scholar
  7. 7.
    S.G. Williamson, Depth-first search and kuratowski subgraphs, Journal of the ACM 31 (1984), no. 4, 681–693.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hubert de Fraysseix
    • 1
  • Patrice Ossona de Mendez
    • 2
  1. 1.UMRCNRSParisFrance
  2. 2.UMRCNRSParisFrance

Personalised recommendations