
Packing directed circuits quarterintegrally
The celebrated ErdősPósa theorem states that every undirected graph tha...
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Parametrised Algorithms for Directed Modular Width
Many wellknown NPhard algorithmic problems on directed graphs resist e...
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Flip distances between graph orientations
Flip graphs are a ubiquitous class of graphs, which encode relations ind...
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Determining a Slater Winner is Complete for Parallel Access to NP
We consider the complexity of deciding the winner of an election under t...
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The Good, the Bad, and the Odd: Cycles in AnswerSet Programs
Backdoors of answerset programs are sets of atoms that represent clever...
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Solutions for Subset Sum Problems with Special Digraph Constraints
The subset sum problem is one of the simplest and most fundamental NPha...
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The Italian domination numbers of some products of directed cycles
An Italian dominating function on a digraph D with vertex set V(D) is de...
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Colouring NonEven Digraphs
A colouring of a digraph as defined by Erdos and NeumannLara in 1980 is a vertexcolouring such that no monochromatic directed cycles exist. The minimal number of colours required for such a colouring of a loopless digraph is defined to be its dichromatic number. This quantity has been widely studied in the last decades and can be considered as a natural directed analogue of the chromatic number of a graph. A digraph D is called even if for every 01weighting of the edges it contains a directed cycle of even total weight. We show that every noneven digraph has dichromatic number at most 2 and an optimal colouring can be found in polynomial time. We strengthen a previously known NPhardness result by showing that deciding whether a directed graph is 2colourable remains NPhard even if it contains a feedback vertex set of bounded size.
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