A note on arbitrarily vertex decomposable graphs
A graph (G) of order (n) is said to be challenge gravel grinder 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