Dominating induced matchings in graphs without a skew star

doi:10.1016/j.jda.2013.11.002

Journal of Discrete Algorithms

Volume 26, May 2014, Pages 45-55

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Abstract

We study the problem of determining whether a graph G has an induced matching that dominates every edge of the graph, which is also known as efficient edge domination. This problem is known to be NP-complete in general graphs, but it can be solved in polynomial time for graphs in some special classes, such as weakly chordal, $P_{7}$ -free or claw-free graphs. In the present paper we extend the polynomial-time solvability of the problem from claw-free graphs to graphs without a skew star, where a skew star is a tree with exactly three vertices of degree 1 being of distance $1, 2, 3$ from the only vertex of degree 3.

Keywords

Dominating induced matching

Efficient edge dominating set

Polynomial-time algorithm

Clique-width

Cited by (0)

¹: Partially supported by EPSRC via the grant EP/J006130/1.

²: The author gratefully acknowledges support from DIMAP – the Center for Discrete Mathematics and its Applications at the University of Warwick, and from EPSRC, grant EP/I01795X/1.