Congestion-free embedding of multiple spanning trees in an arrangement graph

The arrangement graph A_n,k is a generalization of star graph (n-k=1) and more flexible than the star graph. In this paper we consider the embedding of multiple spanning trees in an arrangement graph with the objective of being congestion-free. This is first result to exploit multiple spanning trees in the arrangement graphs. We develop a congestion-free embedding of n-k spanning trees with height 2k-1 in an (n, k)-dimensional arrangement graph