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Results tagged with covering
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user 42586
8
votes
1
answer
246
views
The minimal number of partitions to cover all $k$ tuples
The set $N=\{1, 2, \ldots, 2k\}$ can be partitioned into pairs (e.g $(1,2),(3,4),\ldots,(2k-1,2k)$) in $\frac{(2k)!}{k!2^k}$ ways.
$k$-tuple is subset of size $k$ in $N$. We say that $k$-tuple is co …
- 109k
7
votes
2
answers
419
views
Minimum covers of complete graphs by $4$-cycles
I am interested in coverings of the (edge set of the) complete graph $K_n$ by cycles of length $4$. It is clear that such coverings exist for each $n \ge 4$. I need to find the minimum number of $4$-c …
- 13k