Algorithmic Aspects of Upper Domination
Cristina Bazgan, Ljiljana Brankovic, Katrin Casel, Henning, Fernau, Klaus Jansen, Michael Lampis, Mathieu Liedloff and, J\'er\^ome Monnot, Vangelis Th. Paschos
TL;DR
This paper explores the computational complexity and algorithmic challenges of upper domination in graphs, focusing on maximal minimal dominating sets across various graph classes.
Contribution
It provides a comprehensive classification of upper domination problems, including maximization, minimization, and parameterized variants, on general, bounded degree, and planar graphs.
Findings
Classified the complexity of upper domination problems.
Analyzed upper domination on different graph classes.
Provided algorithmic insights for specific graph types.
Abstract
In this paper we study combinatorial and algorithmic resp. complexity questions of upper domination, i.e., the maximum cardinality of a minimal dominating set in a graph. We give a full classification of the related maximisation and minimisation problems, as well as the related parameterised problems, on general graphs and on graphs of bounded degree, and we also study planar graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems