On the complexity of the dominating induced matching problem in hereditary classes of graphs

• Published in: Discrete Applied Mathematics Vol. 159; no. 7; pp. 521 - 531
• Main Authors: Cardoso, Domingos M., Korpelainen, Nicholas, Lozin, Vadim V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 06.04.2011
• Subjects: Algorithms; Boundaries; Complexity; Computation; Dominating induced matching; Efficient edge dominating set; Graphs; Matching; Mathematical models; Polynomial-time algorithm; Dominating induced matching; Efficient edge dominating set; Polynomial-time algorithm
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2010.03.011

The dominating induced matching problem, also known as efficient edge domination, is the problem of determining whether a graph has an induced matching that dominates every edge of the graph. This problem is known to be NP-complete. We study the computational complexity of the problem in special graph classes. In the present paper, we identify a critical class for this problem (i.e., a class lying on a “boundary” separating difficult instances of the problem from polynomially solvable ones) and derive a number of polynomial-time results. In particular, we develop polynomial-time algorithms to solve the problem for claw-free graphs and convex graphs.