List Supermodular Coloring

This is a preview of subscription content, access via your institution.

References

  1. [1]

    M. Aigner and G. M. Ziegler: Proofs from the Book, Springer-Verlag, Berlin & Heidelberg, 2010.

    Book  MATH  Google Scholar 

  2. [2]

    EGRES: Open problems: http://lemon.cs.elte.hu/egres/open/ (accessed October 28, 2016).

  3. [3]

    T. Fleiner: A fixed-point approach to stable matchings and some applications, Mathematics of Operations Research 28 (2003), 103–126.

    MathSciNet  Article  MATH  Google Scholar 

  4. [4]

    T. Fleiner and Z. Jankó: On weighted kernels of two posets, Order 33 (2016), 51–65.

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    A. Frank and T. Király: A survey on covering supermodular functions, Research Trends in Combinatorial Optimization (W. J. Cook, L. Lovász, and J. Vygen, eds.), Springer-Verlag, 2009, 87–126.

  6. [6]

    A. Frank, T. Király, J. Pap and D. Pritchard: Characterizing and recognizing generalized polymatroids, Mathematical Programming 146 (2014), 245–273.

    MathSciNet  Article  MATH  Google Scholar 

  7. [7]

    A. Frank and é. Tardos: Generalized polymatroids and submodular flows, Mathematical Programming 42 (1988), 489–563.

    MathSciNet  Article  MATH  Google Scholar 

  8. [8]

    D. Gale and L. S. Shapley: College admissions and the stability of marriage, American Mathematical Monthly 69 (1962), 9–15.

    MathSciNet  Article  MATH  Google Scholar 

  9. [9]

    F. Galvin: The list chromatic index of a bipartite multigraph, Journal of Combinatorial Theory, Series B 63 (1995), 153–158.

    MATH  Google Scholar 

  10. [10]

    M. Grötschel, L. Lovász and A. Schrijver: Geometric Algorithms and Combinatorial Optimization (2nd ed.), Springer-Verlag, Berlin, 1993.

    Book  MATH  Google Scholar 

  11. [11]

    R. P. Gupta: An edge-coloration theorem for bipartite graphs with applications, Discrete Mathematics 23 (1978), 229–233.

    MathSciNet  Article  MATH  Google Scholar 

  12. [12]

    S. Iwata, L. Fleischer and S. Fujishige: A combinatorial strongly polynomial algorithm for minimizing submodular functions, Journal of the ACM 48 (2001), 761–777.

    MathSciNet  Article  MATH  Google Scholar 

  13. [13]

    D. Kőnig: Graphok és alkalmazásuk a determinánsok és a halmazok elméletére (Hungarian; Graphs and their application to the theory of determinants and sets), Mathematikai és Természettudományi Értesitő 34 (1916), 104–119.

    MATH  Google Scholar 

  14. [14]

    Y. T. Lee, A. Sidford and S. C.-W. Wong: A faster cutting plane method and its implications for combinatorial and convex optimization, Proc. 56th FOCS, IEEE, 2015, 1049–1065.

    Google Scholar 

  15. [15]

    J. B. Orlin: A faster strongly polynomial time algorithm for submodular function minimization, Mathematical Programming 118 (2009), 237–251.

    MathSciNet  Article  MATH  Google Scholar 

  16. [16]

    B. Sands, N. Sauer and R. Woodrow: On monochromatic paths in edge-coloured digraphs, Journal of Combinatorial Theory, Series B 33 (1982), 271–275.

    MATH  Google Scholar 

  17. [17]

    A. Schrijver: Supermodular colourings, Matroid Theory (L. Lovász and A. Recski, eds.), North-Holland, Amsterdam, 1985, 327–343.

  18. [18]

    A. Schrijver: A combinatorial algorithm minimizing submodular functions in strongly polynomial time, Journal of Combinatorial Theory, Series B 80 (2000), 346–355.

    MATH  Google Scholar 

  19. [19]

    é. Tardos: Generalized matroids and supermodular colourings, in: Matroid Theory (L. Lovász and A. Recski, eds.), North-Holland, Amsterdam, 1985, 359–382.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Satoru Iwata.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Iwata, S., Yokoi, Y. List Supermodular Coloring. Combinatorica 38, 1437–1456 (2018). https://doi.org/10.1007/s00493-017-3670-4

Download citation

Mathematics Subject Classification (2000)

  • 06A07
  • 05C15