
Finding Efficient Domination for P_8Free Bipartite Graphs in Polynomial Time
A vertex set D in a finite undirected graph G is an efficient dominating...
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On Structural Parameterizations of Firefighting
The Firefighting problem is defined as follows. At time t=0, a fire brea...
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Stability of Special Graph Classes
Frei et al. [6] showed that the problem to decide whether a graph is sta...
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Parameterized Complexity of Independent Set in HFree Graphs
In this paper, we investigate the complexity of Maximum Independent Set ...
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Hedonic Seat Arrangement Problems
In this paper, we study a variant of hedonic games, called Seat Arrangem...
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Graph Square Roots of Small Distance from Degree One Graphs
Given a graph class ℋ, the task of the ℋSquare Root problem is to decid...
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Tuning Ranking in Cooccurrence Networks with General Biased Exchangebased Diffusion on Hyperbaggraphs
Cooccurence networks can be adequately modeled by hyperbaggraphs (hb...
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When Maximum Stable Set can be solved in FPT time
Maximum Independent Set (MIS for short) is in general graphs the paradigmatic W[1]hard problem. In stark contrast, polynomialtime algorithms are known when the inputs are restricted to structured graph classes such as, for instance, perfect graphs (which includes bipartite graphs, chordal graphs, cographs, etc.) or clawfree graphs. In this paper, we introduce some variants of cographs with parameterized noise, that is, graphs that can be made into disjoint unions or complete sums by the removal of a certain number of vertices and the addition/deletion of a certain number of edges per incident vertex, both controlled by the parameter. We give a series of FPT Turingreductions on these classes and use them to make some progress on the parameterized complexity of MIS in Hfree graphs. We show that for every fixed t ≥ 1, MIS is FPT in P(1,t,t,t)free graphs, where P(1,t,t,t) is the graph obtained by substituting all the vertices of a fourvertex path but one end of the path by cliques of size t. We also provide randomized FPT algorithms in dartfree graphs and in cricketfree graphs. This settles the FPT/W[1]hard dichotomy for fivevertex graphs H.
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