SEARCH

SEARCH BY CITATION

REFERENCES

  • 1
    O. V. Borodin, Solution of Ringel's problem about vertex bound colouring of planar graphs and colouring of 1-planar graphs, Metody Discret Anal 41 (1984), 1226.
  • 2
    O. V. Borodin, A new proof of the 6-color theorem, J Graph Theory 19 (1995), 507521.
  • 3
    O. V. Borodin, A. V. Kostochka, A. Raspaud, and E. Sopena, Acyclic colouring of 1-planar graphs, Discrete Anal Oper Res 6 (1999), 2035.
  • 4
    R. Bodendiek, H. Schumacher, and K. Wagner, Bemerkungen zu einen Sechsfarbenproblem von G. Ringel, Abh Math Semin Univ Hamburg 53 (1983), 4152.
  • 5
    Z.-Z. Chen, Approximation algorithms for independent sets in map graphs, J Algorithms 41 (2001), 2040.
  • 6
    Z.-Z. Chen, New bounds on the number of edges in a k-map graph, Lect Notes Comput Sci 3106 (2004), 319328.
  • 7
    Z.-Z. Chen, E. Grigni, and C. H. Papadimitriou, Planar map graphs, Proceedings of the Thirtieth Annual ACM symposium on Theory of Computing, May 24–26, 1998, Dallas, TX, pp. 514523.
  • 8
    Z.-Z. Chen, M. Grigni, and C. H. Papadimitriou, Map graphs, J ACM 49 (2002), 127138.
  • 9
    Z.-Z. Chen and M. Kouno, A linear-time algorithm for 7-coloring 1-plane graphs, Algorithmica 43 (2005), 147177.
  • 10
    I. Fabrici and T. Madaras, The structure of 1-planar graphs, Discrete Math 307 (2007), 854865.
  • 11
    M. R. Garey, D. S. Johnson, and L. Stockmeyer, Some simplified NP-complete graph problems, Theor Comp Sci 1 (1976), 237267.
  • 12
    V. P. Korzhik, Minimal non-1-planar graphs, Discrete Math 308 (2008), 13191327.
  • 13
    V. P. Korzhik and Bojan Mohar, Minimal obstructions for 1-immersions and hardness of 1-planarity testing, GD 2008, Lect Notes Comput Sci 5417 (2009), 302312.
  • 14
    G. Ringel, Ein Sechsfarbenproblem auf der Kugel, Abh Semin Univ Hamburg 29 (1965), 107117.
  • 15
    H. Schumacher, Zur Struktur 1-planarer Graphen, Math Nachr 125 (1986), 291300.