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- W2055190873 abstract "A proper vertex coloring of a simple graph $G$ is $k$-forested if the subgraph induced by the vertices of any two color classes is a forest with maximum degree at most $k$. The $k$-forested chromatic number of a graph $G$, denoted by $chi^{a}_{k}(G)$, is the smallest number of colors in a $k$-forested coloring of $G$. In this paper, it is shown that planar graphs with large enough girth do satisfy $chi^{a}_{k}(G)=lceilfrac{Delta(G)}{k}rceil+1$ for all $Delta(G)> kgeq 2$, and $chi^{a}_{k}(G)leq 3$ for all $Delta(G)leq k$ with the bound 3 being sharp. Furthermore, a conjecture on $k$-frugal chromatic number raised in [1] has been partially confirmed." @default.
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- W2055190873 date "2010-10-01" @default.
- W2055190873 modified "2023-10-18" @default.
- W2055190873 title "$k$-forested coloring of planar graphs with large girth" @default.
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- W2055190873 doi "https://doi.org/10.3792/pjaa.86.169" @default.
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