Blocking total dominating sets via edge contractions
Esther Galby, F.M. Mann, Bernard Ries · Theoretical Computer Science · 2021
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 complexity dichotomy for H-free graphs.