Dominating sets reconfiguration under token sliding
Marthe Bonamy (LaBRI), Paul Dorbec, Paul Ouvrard (LaBRI)

TL;DR
This paper studies the reconfiguration problem of dominating sets in graphs, proving PSPACE-completeness in general but polynomial-time solvability in certain graph classes like dually chordal graphs and cographs.
Contribution
It establishes the computational complexity of dominating set reconfiguration under token sliding, showing hardness in some graph classes and efficient algorithms in others.
Findings
PSPACE-complete for split, bipartite, and bounded treewidth graphs
Polynomial-time algorithm for dually chordal graphs and cographs
Reconfiguration problem complexity varies significantly across graph classes
Abstract
Let be a graph and and be two dominating sets of of size . Does there exist a sequence of dominating sets of such that can be obtained from by replacing one vertex with one of its neighbors? In this paper, we investigate the complexity of this decision problem. We first prove that this problem is PSPACE-complete, even when restricted to split, bipartite or bounded treewidth graphs. On the other hand, we prove that it can be solved in polynomial time on dually chordal graphs (a superclass of both trees and interval graphs) or cographs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Distributed systems and fault tolerance · Complexity and Algorithms in Graphs
