Conditional matching preclusion sets

  • Authors:

  • Eddie Cheng;Linda Lesniak;Marc J. Lipman;László Lipták

  • Affiliations:

  • Department of Mathematics and Statistics, Oakland University, 2200 N. Squirrel Road, Rochester, MI 48309, United States;Department of Mathematics and Computer Science, Drew University, Madison, NJ 07940, United States;College of Arts and Sciences, Indiana University, Purdue University Fort Wayne, Fort Wayne, IN 46805, United States;Department of Mathematics and Statistics, Oakland University, 2200 N. Squirrel Road, Rochester, MI 48309, United States

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. In this paper, we look for obstruction sets beyond these sets. We introduce the conditional matching preclusion number of a graph. It is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. We find this number and classify all optimal sets for several basic classes of graphs.