Using edge contractions to reduce the semitotal domination number

Bernard Ries,Felix Mann,Paloma T. Lima,Esther Galby

doi:10.1016/j.tcs.2022.10.020

Using edge contractions to reduce the semitotal domination number

Bernard Ries, Felix Mann + Show 2 more

Open Access

https://doi.org/10.1016/j.tcs.2022.10.020

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Journal: Theoretical Computer Science	Publication Date: Oct 21, 2022
Citations: 2	License type: cc-by

Affiliation: University of Fribourg, IT University of Copenhagen, Helmholtz Center for Information Security

#Edge Contractions #Semitotal Domination + Show 2 more

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Abstract

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.

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