In the graph theory how many paths of length k 1 are there i

In the graph theory,

how many paths of length k 1 are there in Kn?

Solution

As there are (N1)(N2)/2 edges in the complete graph Kn

and each of your paths can cover K edges, the number m of paths must be (N1)(N2)/2K.

If N is odd, this is easily achieved by an Eulerian path cut into pieces of length K.

If N is even, a similar aproach is possible.