Group divisible (K_4-e)-packings with any minimum leave

摘要

A decomposition of $K_{n(g)}\setminus L$, the complete n-partite equipartitegraph with a subgraph L (called the leave) removed, into edge disjoint copiesof a graph G is called a maximum group divisible packing of $K_{n(g)}$ with Gif L contains as few edges as possible. We examine all possible minimum leavesfor maximum group divisible $(K_4-e)$-packings. Necessary and sufficientconditions are established for their existences.