English

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 kk edges, for some fixed k1k \geq 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=1k=1 and obtain in particular a complete complexity dichotomy for monogenic classes.

Keywords

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}
}
R2 v1 2026-06-24T03:59:46.040Z