Abstract
The K i - j packing problem P i, j is defined as follows: Given a graph G and integer k does there exist a set of at least k K i 's in G such that no two of these K i 's intersect in more than j nodes. This problem includes such problems as matching, vertex partitioning into complete subgraphs and edge partitioning into complete subgraphs. In this paper it is shown thhat for i ⩾ 3 and 0⩽ j⩽ i −2 the P i, j problems is NP-complete. Furthermore, the problems remains NP-complete for i⩾3 and 1⩽ j⩽ i −2 for chordal graphs.
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