Defective colorings of graphs in surfaces: Partitions into subgraphs of bounded valency

@article{Cowen1986DefectiveCO,
  title={Defective colorings of graphs in surfaces: Partitions into subgraphs of bounded valency},
  author={Lenore Cowen and Robert Cowen and Douglas R. Woodall},
  journal={Journal of Graph Theory},
  year={1986},
  volume={10},
  pages={187-195}
}
We call a graph (m, k)-colorable if its vertices can be colored with m colors in such a way that each vertex is adjacent to at most k vertices of the same color as itself. For the class of planar graphs, and the class of outerplanar graphs, we determine all pairs (m, k) such that every graph in the class is ( m , k)-colorable. We include an elementary proof (not assuming the truth of the four-color theorem) that every planar graph is (4, 1)-colorable. Finally, we prove that, for each compact… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-4 of 4 references

The Appel-Haken proof of the four-color theorem

  • D. R. Woodall, R. J . Wilson
  • Selected Topics in Graph Theory,
  • 1978

The existence of unavoidable sets of geographically good configurations. lllinois

  • K. Appel, W. Haken
  • J . Math
  • 1976

Lovasz , On decompositions of graphs

  • R. J. Wilson
  • Studia Sci . Math . Hungar .
  • 1969

Haken , The existence of unavoidable sets of geographically good configurations

  • W.
  • lllinois J . Math .

Similar Papers

Loading similar papers…