Algorithmic Aspects of Upper Domination: A Parameterised Perspective

Cristina Bazgan (1) , Ljiljana Brankovic (2) , Katrin Casel , Henning Fernau (3) , Klaus Jansen (4) , Kim-Manuel Klein , Michail Lampis (1) , Mathieu Liedloff (5) , Jérôme Monnot (1) , Vangelis Paschos (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 School of Electrical Engineering and Computer Science
3 Trier University
4 Department of Computer Science [Kiel]
5 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

This paper studies Upper Domination, i.e., the problem of computing the maximum cardinality of a minimal dominating set in a graph, with a focus on parameterised complexity. Our main results include W[1]-hardness for Upper Domination, contrasting FPT membership for the parameterised dual Co-Upper Domination. The study of structural properties also yields some insight into Upper Total Domination. We further consider graphs of bounded degree and derive upper and lower bounds for kernelisation.

Domaines: Algorithme et structure de données [cs.DS]

Cristina Bazgan, Ljiljana Brankovic, Katrin Casel, Henning Fernau, Klaus Jansen, et al.. Algorithmic Aspects of Upper Domination: A Parameterised Perspective. 11th International Conference Algorithmic Aspects in Information and Management (AAIM), Jul 2016, Bergamo, Italy. pp.113-124, ⟨10.1007/978-3-319-41168-2_10⟩. ⟨hal-01367853⟩