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 (nÿ k ˆ 1), but also more ̄exible. 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…nÿ k† edge disjoint spanning trees in an arrangement graph, where each congestion-free spanning tree's height is 2k ÿ 1. Our scheme is based on a subgraphpartitioning scheme. First, we construct 2…nÿ k† base spanning trees in every Anÿk‡2;2. Then, we recursively construct 2…nÿ k† spanning trees from every Anÿk‡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 Anÿk‡2;2 are fully utilized. Ó 2001 Published by Elsevier Science B.V. All rights reserved.