2021/07/08 by Galby, Esther, Lima, Paloma T., Mann, Felix +1
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.03755
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.