Blocking total dominating sets via edge contractions

Abstract

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(${\gamma }_t$)). 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.