70
Views
0
CrossRef citations to date
0
Altmetric
Articles

On the existence of k-kernels in digraphs and in weighted digraphs

, & (Communicated by)
Pages 201-215 | Received 24 Aug 2009, Accepted 30 Aug 2010, Published online: 10 Mar 2020

References

  • J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications, Springer-Verlag, New York, 2002.
  • J. Bang-Jensen and J. Huang, Quasi-transitive digraphs, J. Graph Theory, 20(2) (1995), 141–161.
  • C. Berge, Graphs, North-Holland, Amsterdam 1985.
  • C. Berge and P. Duchet, Recent problems and results about kernels in directed graphs, Discrete Mathematics, 86 (1990), 27–31.
  • J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, North-Holland, Amsterdam, 1976.
  • R. Diestel, Graph Theory 3rd Edition, Springer-Verlag, Heidelberg, New York, 2005.
  • H. Galeana-Sánchez, On the existence of kernels and h-kernels in directed graphs, Discrete Mathematics, 110 (1992), 251–255.
  • H. Galeana-Sánchez and C. Hernández-Cruz, Cyclically k-partite digraphs and k-kernels, Accepted in Discussiones Mathematicae Graph Theory, 2010.
  • H. Galeana-Sánchez and C. Hernández-Cruz, k-kernels in generalized transitive digraphs, Accepted in Discussiones Mathematicae Graph Theory, 2010.
  • M. Kucharska and M. Kwaśnik, On (k, l)-kernels of special superdigraphs of Pm and Cm, Discuss. Math. Graph Theory, 21(1) (2001), 95–109.
  • M. Kwaśnik, On (k, l)-kernels on graphs and their products, Doctoral dissertation, Technical University of Wroclaw, Wroclaw, 1980.
  • M. Kwaśnik, The Generalizaton of Richardson's Theorem, Discussiones Mathematicae, 4 (1981), 11–14.
  • M. Richardson, On Weakly Ordered Systems, Bull. Amer. Math. Soc., 52 (1946), 113–116.
  • A. Sánchez-Flores, A counterexample to a generalization of Richardson's theorem, Discrete Mathematics, 65 (3) (1987), 319–320.
  • J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1953.
  • W. Szumny, A. Włoch and I. Włoch, On the existence and on the number of (k, l)-kernels in the lexicographic product of graphs, Discrete Mathematics, 308(20) (2008), 4616–4624.
  • W. Szumny, A. Wloch and I. Włoch, On (k, l)-kernels in D-join of digraphs, Discussiones Mathematicae Graph Theory, 27 (2007), 457–470.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.