
Decremental Optimization of Dominating Sets Under Reachability Constraints
Given a dominating set, how much smaller a dominating set can we find th...
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Budgeted Dominating Sets in Uncertain Graphs
We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, ...
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Twinwidth and polynomial kernels
We study the existence of polynomial kernels, for parameterized problems...
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New Results on Directed Edge Dominating Set
We study a family of generalizations of Edge Dominating Set on directed ...
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Characterizing and decomposing classes of threshold, split, and bipartite graphs via 1Sperner hypergraphs
A hypergraph H is said to be 1Sperner if for every two hyperedges the s...
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The eternal dominating set problem for interval graphs
We prove that, in games in which all the guards move at the same turn, t...
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On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets
In a reconfiguration version of an optimization problem Q the input is a...
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Parameterized algorithms for locatingdominating sets
A locatingdominating set D of a graph G is a dominating set of G where each vertex not in D has a unique neighborhood in D, and the LocatingDominating Set problem asks if G contains such a dominating set of bounded size. This problem is known to be ππ―ππΊππ½ even on restricted graph classes, such as interval graphs, split graphs, and planar bipartite subcubic graphs. On the other hand, it is known to be solvable in polynomial time for some graph classes, such as trees and, more generally, graphs of bounded cliquewidth. While these results have numerous implications on the parameterized complexity of the problem, little is known in terms of kernelization under structural parameterizations. In this work, we begin filling this gap in the literature. Our first result shows that LocatingDominating Set is πΆ[1]ππΊππ½ when parameterized by the size of a minimum clique cover. We present an exponential kernel for the distance to cluster parameterization and show that, unless ππ―βπΌπππ―/πππ π, no polynomial kernel exists for LocatingDominating Set when parameterized by vertex cover nor when parameterized by distance to clique. We then turn our attention to parameters not bounded by either of the previous two, and exhibit a linear kernel when parameterizing by the max leaf number; in this context, we leave the parameterization by feedback edge set as the primary open problem in our study.
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