Graph partitions with minimum degree constraints

Given a graph with n nodes and minimum degree δ, we give a polynomial time algorithm that constructs a partition of the nodes of the graph into two sets X and Y such that the sum of the minimum degrees in X and in Y is at least δ and the cardinalities of X and Y differ by at most δ (δ + 1 if n ≠ δ (mod 2)). The existence of such a partition was shown by Sheehan (1988).