Given two k-graphs H and F, a perfect F-packing in H is a collection of vertex-disjoint copies of F in H which together cover all the vertices in H. In the case when F is a single edge, a perfect F-packing is simply a perfect matching. For a given fixed F, it is often the case that the decision problem whether an n-vertex k-graph H contains a perfect F-packing is NP-complete. Indeed, if $k\ge 3$, the corresponding problem for perfect matchings is NP-complete [17], [7] whilst if $k=2$ the problem is NP-complete in the case when F has a component consisting of at least 3 vertices [14].

In this paper we give a general tool which can be used to determine classes of (hyper)graphs for which the corresponding decision problem for perfect F-packings is polynomial time solvable. We then give three applications of this tool: (i) Given $1\le \ell \le k-1$, we give a minimum ℓ-degree condition for which it is polynomial time solvable to determine whether a k-graph satisfying this condition has a perfect matching; (ii) Given any graph F we give a minimum degree condition for which it is polynomial time solvable to determine whether a graph satisfying this condition has a perfect F-packing; (iii) We also prove a similar result for perfect K-packings in k-graphs where K is a k-partite k-graph.

For a range of values of $\ell ,k$ (i) resolves a conjecture of Keevash, Knox and Mycroft [20]; (ii) answers a question of Yuster [47] in the negative; whilst (iii) generalises a result of Keevash, Knox and Mycroft [20]. In many cases our results are best possible in the sense that lowering the minimum degree condition means that the corresponding decision problem becomes NP-complete.

给定两个ķ -graphs ^ h和˚F，完美˚F在分装^ h是顶点不相交的副本的集合˚F在^ h一起覆盖所有顶点^ h。在F是单边的情况下，完美的F包装只是完美的匹配。对于给定的固定F，通常情况下，n-顶点k图H是否包含理想F堆积的决策问题是NP完全的。确实，如果$ķ\ge 3$，则完美匹配的相应问题是NP完全[17]，[7]，而如果 $ķ=2$当F的分量至少由3个顶点组成时，问题是NP完全的[14]。

在本文中，我们提供了一种通用工具，可用于确定（超）图的类，对于这些类，理想的F堆积的相应决策问题是多项式时间可解的。然后，我们给出该工具的三个应用：（i）给定$\mathrm{1个}\le \ell \le ķ-\mathrm{1个}$，我们给出一个最小ℓ度条件，对于该条件，可以通过多项式时间来确定满足该条件的k图是否具有完美匹配；（ii）给定任何图F，我们给出一个最小次数条件，对于该条件，可以确定多项式时间，以确定满足该条件的图是否具有理想的F堆积；（三）我们还证明了完美类似的结果ķ在-packings ķ -graphs其中ķ是ķ -partite ķ -图。

对于以下范围的值 $\ell ，ķ$（i）解决了Keevash，Knox和Mycroft的猜想[20]；（ii）否定回答Yuster [47]的问题；（iii）概括了Keevash，Knox和Mycroft的结果[20]。在许多情况下，从降低最低程度条件意味着相应的决策问题变为NP完全的意义上说，我们的结果是最好的。