A (k,τ)-regular set in a graph is a subset of vertices inducing a k-regular subgraph and such that each vertex not in the set has exactly τ neighbours in it.
We will present a new algorithm for the determination of (0,2)-regular sets as well as its application to the determination of maximum matchings in arbitrary graphs.
In this paper, relevant results about the determination of ( κ , τ )- regular
sets, using the main eigenvalues of a graph, are reviewed and some results about the
determination of (0,2)-regular sets are introduced. An algorithm for that purpose is
also described. As an illustration, this algorithm is applied to the determination of
maximum matchings in arbitrary graphs.
