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# 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} }

- Published 2010 in SIAM J. Discrete Math.
DOI:10.1137/090780894

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