Using edge contractions to reduce the semitotal domination number
Combinatorics
2021-07-09 v1 Discrete Mathematics
Abstract
In this paper, we consider the problem of reducing the semitotal domination number of a given graph by contracting edges, for some fixed . 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 and obtain in particular a complete complexity dichotomy for monogenic classes.
Cite
@article{arxiv.2107.03755,
title = {Using edge contractions to reduce the semitotal domination number},
author = {Esther Galby and Paloma T. Lima and Felix Mann and Bernard Ries},
journal= {arXiv preprint arXiv:2107.03755},
year = {2021}
}