A (k / q, d) defective circular coloring of a simple graph G = (V, E) is a function c : V → (0, ... , κ ― 1} such that each vertex v ∈ V is adjacent to at most d vertices u where q ≤ |c(v) ― c(u)| ≤ κ ― q does not hold. If such a defective circular coloring exists, we say G is (κ / q, d) colorable. When q = 1 and d = 0, defective circular coloring conforms to the usual version of graph coloring. In this paper, we improve a previous result on defective circular coloring of planar graphs and present several other related results. Several open problems are stated.
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