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Packing and covering of the complete graph. II: The trees of order six. (English) Zbl 0578.05013
[For part I, see J. Comb. Theory, Ser. A. 35, 213-243 (1983; Zbl 0521.05053).]
It is shown that the maximal number of pairwise edge disjoint trees of order six in the complete graph $$K_ n$$, and the minimum number of trees of order six, whose union is $$K_ n$$ are [$$\frac{n(n-1)}{10}]$$ and $$\{$$ $$\frac{n(n-1)}{10}\}$$, $$n\geq 9$$, respectively. ([x] denotes the largest integer not exceeding x and $$\{$$ $$x\}$$ the least integer not less than x.)
Reviewer: J.Schwarze

##### MSC:
 05C05 Trees 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C35 Extremal problems in graph theory