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

Authors:
Domingos M. Cardoso;Nicholas Korpelainen;Vadim V. Lozin
Affiliations:
Departamento de Matemática, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal;DIMAP and Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom;DIMAP and Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

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.