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Packing and covering of the complete graph. IV: The trees of order seven. (English) Zbl 0796.05074
[For Part I, Part II and Part III see Zbl 0608.05028, Zbl 0578.05013 and Zbl 0699.05044, respectively.]
The investigation of the packing number $$P(n,H)$$, i.e. the maximal number of pairwise edge disjoint subgraphs of $$K_ n$$ isomorphic to $$H$$, and of the covering number $$C(n,H)$$, i.e. the minimum number of subgraphs of $$K_ n$$ isomorphic to $$H$$ and covering $$K_ n$$, is continued. For $$H$$ being any tree of order seven and $$n \geq 11$$ it is shown that $$P(n,H) = \lfloor {n(n-1) \over 12} \rfloor$$ and $$C(n,H) = \lceil {n(n-1) \over 12} \rceil$$.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C05 Trees
##### Keywords:
complete graph; packing number; covering number; covering; tree