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

The arrangement graph A n, 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 tree's height is 2 k−1. Our scheme is based on a subgraph-partitioning scheme. First, we construct 2( n− k) base spanning trees in every A n− k+2,2 . Then, we recursively construct 2( n− k) spanning trees from every A n− k+2,2 up to A n, k by a bottom-up approach. This is a near-optimal result since all of possible edges in the base subarrangement A n− k+2,2 are fully utilized.