Isolation of Matchings via Chinese Remaindering

In this paper we investigate the question whether a perfect matching can be isolated by a weighting scheme using Chinese Remainder Theorem (short: CRT). We give a systematical analysis to a method based on CRT suggested by Agrawal in a CCC’03-paper for testing perfect matchings. We show that this desired test-procedure is based on a deterministic weighting scheme which can be generalized in a natural way to a scheme for isolating a perfect matching in the graph. Thereby we give a new insight into the topic about deterministic isolations of perfect matchings by showing necessary and sufficient conditions for a potential isolation. Moreover, we show that if the considered weighting scheme by using CRT for isolating perfect matchings works, then the maximum matching problem can be solved completely in NC. This is a generalization of the NC-algorithm showed in [Hoa10] for the maximum matching problem for bipartite planar graphs.