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We consider conflict-free colorings of graph neighborhoods: Each vertex of the graph must be assigned a color so that for each vertex v there is at least one color appearing exactly once in the neighborhood of v. The goal is to minimize the number of used colors. We consider both the case of closed neighborhoods, when the neighborhood of a node includes the node itself, and the case of open neighborhoods...
We consider the $$k$$ k -strong conflict-free ( $$k$$ k -SCF) coloring of a set of points on a line with respect to a family of intervals: Each point on the line must be assigned a color so that the coloring is conflict-free in the following sense: in every interval $$I$$ I of the family there are at least $$k$$ k colors each appearing exactly once in $$I$$ I...
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