Abstract
We describe O(n) time algorithms for finding the minimum weighted dominating induced matching of chordal, dually chordal, biconvex, and claw-free graphs. For the first three classes, we prove tight O(n) bounds on the maximum number of edges that a graph having a dominating induced matching may contain. By applying these bounds, countings and employing existing O(n + m) time algorithms we show that they can be reduced to O(n) time. For claw–free graphs, we describe an algorithm based on that by Cardoso, Korpelainen and Lozin [4], for solving the unweighted version of the problem, which decreases its complexity from O(n 2) to O(n), while additionally solving the weighted version.
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Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L. (2014). O(n) Time Algorithms for Dominating Induced Matching Problems. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_35
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DOI: https://doi.org/10.1007/978-3-642-54423-1_35
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