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# 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} }

- Published 1986 in Journal of Graph Theory
DOI:10.1002/jgt.3190100207

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 compactâ€¦Â CONTINUE READING