Abstract
A graph is uniquelyk-arborable if its point-arboricity isk and there is only one acyclic partition of its point set intok subsets. Several properties of uniquelyk-arborable graphs are presented. One such property is that uniquelyk-arborable graphs are (k−1)-connected. Furthermore, it is shown that for any positive integerk there is a uniquelyk-arborable graph which is notk-connected.
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