Arbitrarily vertex decomposable graph

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Arbitrarily vertex decomposable graphпроизвольно вершинно разложимый граф.

A graph \,G of order \,n is said to be arbitrarily vertex decomposable, if for each sequence (n_{1}, \ldots, n_{k}) of positive integers such that n_{1} + \ldots + n_{k} = n there exists a partition (V_{1}, \ldots, V_{k}) of the vertex set of \,G such that, for each i \in \{1, \ldots, k\}, V_{i} induces a connected subgraph of \,G on \,n_{i} vertices.

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