The Balanced Decomposition Number and Vertex Connectivity

@article{Fujita2010TheBD,
  title={The Balanced Decomposition Number and Vertex Connectivity},
  author={Shinya Fujita and Henry Liu},
  journal={SIAM J. Discrete Math.},
  year={2010},
  volume={24},
  pages={1597-1616}
}
The balanced decomposition number f(G) of a graph G was introduced by Fujita and Nakamigawa [Discr. Appl. Math., 156 (2008), pp. 3339-3344]. A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, such that there is the same number of vertices in each colour. Then, f(G) is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪̇ · · · ∪̇Vr such that, for every i, Vi induces a connected subgraph… CONTINUE READING