Strong matching preclusion

Authors:
Jung-Heum Park;Insung Ihm
Affiliations:
School of Computer Science and Information Engineering, The Catholic University of Korea, Bucheon, Republic of Korea;Department of Computer Science and Engineering, Sogang University, Seoul, Republic of Korea
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

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.