In this paper, we study the problem of deciding whether the total domination number of a given graph G can be reduced using exactly one edge contraction (called 1-Edge Contraction(γt)). We focus on several graph classes and determine the computational complexity of this problem. By putting together these results, we manage to obtain a complete dichotomy for H-free graphs.
@article{arxiv.2009.08806,
title = {Blocking total dominating sets via edge contractions},
author = {Esther Galby and Felix Mann and Bernard Ries},
journal= {arXiv preprint arXiv:2009.08806},
year = {2020}
}