# Exact defective colorings of graphs

@article{Cumberbatch2021ExactDC, title={Exact defective colorings of graphs}, author={James Cumberbatch and Juho Lauri and Christodoulos Mitillos}, journal={ArXiv}, year={2021}, volume={abs/2109.05255} }

An exact (k, d)-coloring of a graph G is a coloring of its vertices with k colors such that each vertex v is adjacent to exactly d vertices having the same color as v. The exact d-defective chromatic number, denoted χd (G), is the minimum k such that there exists an exact (k, d)-coloring of G. In an exact (k, d)-coloring, which for d = 0 corresponds to a proper coloring, each color class induces a d-regular subgraph. We give basic properties for the parameter and determine its exact value for…

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