Let $K_n$ denote the complete graph of order $n$. Let $G_1 , G_2 , \cdots , G_r$ denote complete bipartite sub-graphs of $K_n$ . Suppose that the graphs $G_1 , G_2 , \cdots , G_r$ are edge disjoint and between them contain all of the edges of $K_n$ . Then we say that $G_1 , G_2 , \cdots , G_r$ form a decomposition of $K_n$.
It is easy to construct decomposition of $K_n$ for which $r = n - 1$ and $G_1 , G_2 , \cdots , G_{n-1}$ is $K_{1,n-1} , K_{1,n-2} , . . . , K_{1,1}$ .
Here $K_{m,n}$ is a complete bipartite sub-graph.
I am having confusion in understanding the definition and the example.
Specifically this line *Suppose that the graphs $G_1 , G_2 , \cdots , G_r$ are edge disjoint and between them contain all of the edges of $K_n$ *