vix.ing · top · new · best · stats · spec

The complexity of blocking (semi)total dominating sets with edge contractions

2022/05/25 by Esther Galby, Galby, Esther
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Optimization and Search Problems

paper · pdf · doi:10.48550/arxiv.2205.12821

openalex publication_date 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of reducing the (semi)total domination number of graph by one by contracting edges. It is known that this can always be done with at most three edge contractions and that deciding whether one edge contraction suffices is an NP-hard problem. We show that for every fixed k ∈ \2,3\, deciding whether exactly k edge contractions are necessary is NP-hard and further provide for k=2 complete complexity dichotomies on monogenic graph classes.

Related