
Parameterized Complexity of Geodetic Set
A vertex set S of a graph G is geodetic if every vertex of G lies on a s...
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On the (Parameterized) Complexity of Almost Stable Marriage
In the Stable Marriage problem. when the preference lists are complete, ...
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Feedback Edge Sets in Temporal Graphs
The classical, lineartime solvable Feedback Edge Set problem is concern...
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Approximating Stable Matchings with Ties of Bounded Size
Finding a stable matching is one of the central problems in algorithmic ...
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A note on the complexity of Feedback Vertex Set parameterized by mimwidth
We complement the recent algorithmic result that Feedback Vertex Set is ...
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On the fixedparameter tractability of the maximum connectivity improvement problem
In the Maximum Connectivity Improvement (MCI) problem, we are given a di...
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Computing Maximum Matchings in Temporal Graphs
We study the computational complexity of finding maximumcardinality tem...
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Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters
We continue and extend previous work on the parameterized complexity analysis of the NPhard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixedparameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]hard to compute a maximumcardinality stable matching for acceptability graphs of bounded treedepth, bounded treecut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we `only' ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixedparameter tractability with respect to treecut width but not with respect to treedepth. On the positive side, we also provide fixedparameter tractability results for the parameter feedback edge set number.
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