
Width Parameterizations for Knotfree Vertex Deletion on Digraphs
A knot in a directed graph G is a strongly connected subgraph Q of G wit...
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Witnessing subsystems for probabilistic systems with low tree width
A standard way of justifying that a certain probabilistic property holds...
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Colouring NonEven Digraphs
A colouring of a digraph as defined by Erdos and NeumannLara in 1980 is...
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Comparing Linear Width Parameters for Directed Graphs
In this paper we introduce the linear cliquewidth, linear NLCwidth, ne...
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CliqueWidth and Directed Width Measures for AnswerSet Programming
Disjunctive Answer Set Programming (ASP) is a powerful declarative progr...
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Rooting for phylogenetic networks
This paper studies the relationship between undirected (unrooted) and di...
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Minimum 0Extension Problems on Directed Metrics
For a metric μ on a finite set T, the minimum 0extension problem 0Ext[...
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Parametrised Algorithms for Directed Modular Width
Many wellknown NPhard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAGwidth, Kellywidth and many others. While these focus on measuring how close a digraph is to an oriented tree resp. a directed acyclic graph, in this paper, we investigate directed modular width as a parameter, which is closer to the concept of cliquewidth. We investigate applications of modular decompositions of directed graphs to a wide range of algorithmic problems and derive FPTalgorithms for several wellknown digraphspecific NPhard problems, namely minimum (weight) directed feedback vertex set, minimum (weight) directed dominating set, digraph colouring, directed Hamiltonian path/cycle, partitioning into paths, (capacitated) vertexdisjoint directed paths, and the directed subgraph homeomorphism problem. The latter yields a polynomialtime algorithm for detecting topological minors in digraphs of bounded directed modular width. Finally we illustrate that also other structural digraph parameters, such as the directed pathwidth and the cyclerank can be computed efficiently using directed modular width as a parameter.
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