Algorithms for Weighted Independent Transversals and Strong Colouring

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