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- W3129896241 abstract "For a fixed simple digraph F and a given simple digraph D, an F-free k-coloring of D is a vertex-coloring in which no induced copy of F in D is monochromatic. We study the complexity of deciding for fixed F and k whether a given simple digraph admits an F-free k-coloring. Our main focus is on the restriction of the problem to planar input digraphs, where it is only interesting to study the cases k∈{2,3}. From known results it follows that for every fixed digraph F whose underlying graph is not a forest, every planar digraph D admits an F-free 2-coloring, and that for every fixed digraph F with Δ(F)≥3, every oriented planar graph D admits an F-free 3-coloring. We show in contrast, that • if F is an orientation of a path of length at least 2, then it is NP-hard to decide whether an acyclic and planar input digraph D admits an F-free 2-coloring. • if F is an orientation of a path of length at least 1, then it is NP-hard to decide whether an acyclic and planar input digraph D admits an F-free 3-coloring." @default.
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- W3129896241 date "2022-10-01" @default.
- W3129896241 modified "2023-10-02" @default.
- W3129896241 title "Colorings of oriented planar graphs avoiding a monochromatic subgraph" @default.
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- W3129896241 doi "https://doi.org/10.1016/j.dam.2022.05.015" @default.
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