A Note on the Vertex Arboricity of a Graph

@article{Hakimi1989ANO,
  title={A Note on the Vertex Arboricity of a Graph},
  author={S. Louis Hakimi and Edward F. Schmeichel},
  journal={SIAM J. Discrete Math.},
  year={1989},
  volume={2},
  pages={64-67}
}
The vertex arboricity a(G) of a graph G is the minimum number of subsets into which the vertices ofG can be partitioned so that each subset induces an acyclic graph. A characterization ofplanar graphs G is given for which a(G) 2, thereby answering a question of Griinbaum [Israel J. Math., 14 (1973), pp. 390-408 ]. The characterization is in terms of the dual graph G*. As a corollary, a theorem of Stein that characterizes maximal planar graphs G with a(G) 2 is obtained. This latter result… CONTINUE READING

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