A note on extreme sets - Radosław Cymer (Electronic Journal of Graph Theory and Applications (EJGTA), 2017)
In decomposition theory, extreme sets have been studied extensively due to its connection to perfect matchings in a graph. In this paper, we first define extreme sets with respect to degree-matchings and next investigate some of their properties. In particular, we prove the generalized Decomposition Theorem and give a characterization for the set of all extreme vertices in a graph.