Using edge contractions to reduce the semitotal domination number

07/08/2021

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by   Esther Galby, et al.

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In this paper, we consider the problem of reducing the semitotal domination number of a given graph by contracting k edges, for some fixed k ≥ 1. We show that this can always be done with at most 3 edge contractions and further characterise those graphs requiring 1, 2 or 3 edge contractions, respectively, to decrease their semitotal domination number. We then study the complexity of the problem for k=1 and obtain in particular a complete complexity dichotomy for monogenic classes.