We give an efficient algorithm that, given a graph G and a partition V1,…,Vm of its vertex set, finds either an independent transversal (an independent set {v1,…,vm} in G such that ${v_i} \in {V_i}$ for each i), or a subset ${\cal B}$ of vertex classes such that the subgraph of G induced by $\bigcup\nolimits_{\cal B}$ has a small dominating set. A non-algorithmic proof of this result has been known for a number of years and has been used to solve many other problems. Thus we are able to give algorithmic versions of many of these applications, a few of which we describe explicitly here.

中文翻译：

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有效地寻找独立的横向

我们给出了一个有效的算法，给定一个图G和一个分区五1,…,五米其顶点集，找到任一独立横向（一个独立的集合 {v1,…,v米} 在G这样${v_i} \in {V_i}$对于每个一世) 或子集${\cal B}$顶点类的子图G由...介绍$\bigcup\nolimits_{\cal B}$有一个小的支配集。该结果的非算法证明已为人所知多年，并已用于解决许多其他问题。因此，我们能够给出许多这些应用程序的算法版本，其中一些我们在这里明确描述。