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

Publikationstyp
Journal Article
Date Issued
2023-03-16
Sprache
English
Author(s)
Galby, Esther  
Institut
Algorithmen und Komplexität E-11  
TORE-URI
http://hdl.handle.net/11420/15025
Journal
Theoretical computer science  
Volume
950
Article Number
113678
Citation
Theoretical Computer Science (2023)
Publisher DOI
10.1016/j.tcs.2022.12.028
Scopus ID
2-s2.0-85147979537
ArXiv ID
2205.12821
Publisher
Elsevier
We consider the problem of reducing the (semi)total domination number of a 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.
Subjects
Blocker problem
Edge contraction
H-free graphs
Semitotal domination number
Total domination number
DDC Class
004: Informatik
510: Mathematik