Strong matching preclusion
The matching preclusion problem, introduced by Brigham et al. [R.C. Brigham, F. Harary, E.C. Violin, and J. Yellen, Perfect-matching preclusion, Congressus Numerantium 174 (2005) 185-192], studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible. Extending this concept, we consider a more general matching preclusion problem, called the strong matching preclusion, in which deletion of vertices is additionally permitted. We establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs. (C) 2011 Elsevier B.V. All rights reserved.
matching preclusion perfect and almost perfect matching vertex and/or edge deletion restricted hypercube-like graph recursive circulant