Packing and covering of the complete graph. IV: The trees of order seven. (English) Zbl 0796.05074

Roditty, Y.

Ars Comb. 35, 33-64 (1993).

[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 \(C(n,H) = \lceil {n(n-1) \over 12} \rceil\).

Reviewer: G.Wegner (Dortmund)

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