Planar kernel and grundy with d≤3, dout≤2, din≤2 are NP-complete

@article{Fraenkel1981PlanarKA,
  title={Planar kernel and grundy with d≤3, dout≤2, din≤2 are NP-complete},
  author={Aviezri S. Fraenkel},
  journal={Discrete Applied Mathematics},
  year={1981},
  volume={3},
  pages={257-262}
}
It is proved that the questions whether a finite digraph G has a kernel K or a Sprague-Grundy function g are NP-complete even if G is a cyclic planar digraph with degree constraints dOut(u)s 2, d,,(u) ~2 and d(u) 2 3. These results are best possible (if P f NP) in the sense that if any of the constraints is tightened, there are polynomial algorithms which either compute K and g or show that they do not exist. The proof uses a single reduction from planar 3.satisfiability for both problems. 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-5 of 5 references

Having a Grundy-numbering is NP-complete

  • J. van Leeuwen
  • Report No. 207,
  • 1976

Graphs and Hypergraphs, translated by E

  • C. Berge
  • Minieka (North-Holland, Amsterdam,
  • 1973

On the computational complexity of finding a kernel, Report No. CRM-300

  • V. Chvatal
  • Centre de Recherches Mathematiques, Universite de…
  • 1973
2 Excerpts

Similar Papers

Loading similar papers…