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arXiv · 2009.08806

Blocking total dominating sets via edge contractions

Esther Galby·Felix Mann·Bernard Ries
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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.

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Esther Galby, Felix Mann, Bernard Ries. 2020-09-18. Blocking total dominating sets via edge contractions. https://arxiv.org/abs/2009.08806

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