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A graph G=(V,E) of order n is called arbitrarily partitionable, or AP for short, if given any sequence of positive integers n1,…,nk summing up to n, we can always partition V into subsets V1,…,Vk of sizes n1,…,nk, resp., inducing connected subgraphs in G. If additionally G is minimal with respect to this property, i.e. it contains no AP spanning subgraph, we call it a minimal AP-graph. It has been...
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