# Finding Independent Transversals Efficiently

We give an efficient algorithm that, given a graph G and a partition V_1,...,V_m of its vertex set, finds either an independent transversal (an independent set {v_1,...,v_m} in G such that v_i∈ V_i for each i), or a subset B of vertex classes such that the subgraph of G induced by B has a small dominating set. A non-algorithmic proof of this result has been known for a number of years and has been applied 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.

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