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Packings by cliques and by finite families of graphs. (English) Zbl 0582.05046
If F is a family of connected graphs and G is a graph, then an F-packing of G is a subgraph of G each component of which belongs to F. This paper contains a polynomially bounded algorithm for finding an F-packing of G which as many vertices as possible when F contains \(K_ 2\) and all other graphs in F are hypomatchable, i.e., the deletion of any vertex leaves a graph with a perfect matching. If F does not contain \(K_ 2\), then the problem of finding an F-packing with as many vertices as possible is often NP-complete. This is shown to be the case when F consists of complete graphs of order at least 3 or when F consists of cycles of length at least 6.

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C35 Extremal problems in graph theory
68R10 Graph theory (including graph drawing) in computer science
Full Text: DOI
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