
Computing Subset Feedback Vertex Set via Leafage
Chordal graphs are characterized as the intersection graphs of subtrees ...
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Finding cuts of bounded degree: complexity, FPT and exact algorithms, and kernelization
A matching cut is a partition of the vertex set of a graph into two sets...
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Computational Complexity of Testing Proportional Justified Representation
We consider a committee voting setting in which each voter approves of a...
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Complexity of computing the antiRamsey numbers
The antiRamsey numbers are a fundamental notion in graph theory, introd...
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Finding a Shortest Even Hole in Polynomial Time
An even (respectively, odd) hole in a graph is an induced cycle with eve...
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Minimizing and Computing the Inverse Geodesic Length on Trees
The inverse geodesic length (IGL) of a graph G=(V,E) is the sum of inver...
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On Happy Colorings, Cuts, and Structural Parameterizations
We study the Maximum Happy Vertices and Maximum Happy Edges problems. Th...
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LengthBounded Cuts: Proper Interval Graphs and Structural Parameters
In the presented paper we study the LengthBounded Cut problem for special graph classes as well as from a parameterizedcomplexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set of edges F of size at most β such that every stpath of length at most λ in G contains some edge in F. Bazgan et al. conjectured that LengthBounded Cut admits a polynomialtime algorithm if the input graph G is a proper interval graph. We confirm this conjecture by showing a dynamicprogramming based polynomialtime algorithm. We strengthen the W[1]hardness result of Dvořák and Knop. Our reduction is shorter, seems simpler to describe, and the target of the reduction has stronger structural properties. Consequently, we give W[1]hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that LengthBounded Cut is W[1]hard for the feedback vertex number. Both our hardness results complement known XP algorithms.
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