An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a given vertex partition, which have been used over the years to solve many combinatorial problems. Some of these IT existence theorems have algorithmic proofs, but there remains a gap between the best bounds given by nonconstructive results, and those obtainable by efficient algorithms. Recently, Graf and Haxell (2018) described a new (deterministic) algorithm that asymptotically closes this gap, but there are limitations on its applicability. In this paper we develop a randomized version of this algorithm that is much more widely applicable, and demonstrate its use by giving efficient algorithms for two problems concerning the strong chromatic number of graphs.

翻译：在带有给定顶点分区的图形中,独立的横贯(IT)是一个独立的数据集,由每个分区类中的一个顶点组成。对于在特定图表中存在带有给定顶点分区的信息技术,已经知道几个充分的条件,在特定图表中有一个带有给定的顶点分区,多年来一直用它来解决许多组合问题。有些信息技术存在的理论有算法证明,但非建设性结果给定的最佳界限与高效算法所能获取的界限之间仍有差距。最近,Graf和Haxell(2018年)描述了一种新的(非定点性)算法,这种算法无一例外地缩小了这一差距,但对其适用性是有限制的。在本文中,我们开发了这种算法的随机化版本,该版本应用范围要广得多,并且通过提供高效的算法来证明它用于两个与图表的强色数有关的问题。