Fall coloring of graphs I

@article{Balakrishnan2010FallCO,
  title={Fall coloring of graphs I},
  author={Rangaswami Balakrishnan and T. Kavaskar},
  journal={Discuss. Math. Graph Theory},
  year={2010},
  volume={30},
  pages={385-391}
}
A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number f(G) of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, (G) f(G). In this paper, we show the existence of an innite family of graphs G with prescribed values for (G) and f(G). We also obtain the smallest non-fall… 

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