Congestion-free embedding of 2(n-k) spanning trees in an arrangement graph

The arrangement graph An,k is not only a generalization of star graph (n-k=1), but also more flexible. In this investigation, we elucidate the problem of embedding of multiple spanning trees in an arrangement graph with the objective of congestion-free. This result is to report how to exploit 2(n-k) edge disjoint spanning trees in an arrangement graph, where each congestion-free spanning treeʹs height is 2k-1. Our scheme is based on a subgraph-partitioning scheme. First, we construct 2(n-k) base spanning trees in every An-k+2,2. Then, we recursively construct 2(n-k) spanning trees from every An-k+2,2 up to An,k by a bottom-up approach. This is a near-optimal result since all of possible edges in the base subarrangement An-k+2,2 are fully utilized.