Directed Path-Width of Sequence Digraphs

Gurski, Frank; Rehs, Carolin; Rethmann, Jochen

doi:10.1007/978-3-030-04651-4_6

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…Furthermore the directed path-width can be computed in time 3 τ (und(G)) • |V | O (1) , where τ (und (G)) denotes the vertex cover number of the underlying undirected graph of G, by [50]. For sequence digraphs with a given decomposition into k sequence the directed path-width can be computed in time O(k • (1 + N ) k ), where N denotes the maximum sequence length [35]. Further the directed path-width (and also the directed tree-width) can be computed in linear time for directed co-graphs [34].…”

Section: Directed Path-widthmentioning

confidence: 99%

Comparing Linear Width Parameters for Directed Graphs

Gurski

Rehs

2019

Theory Comput Syst

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In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width, and linear rank-width for directed graphs. We compare these parameters with each other as well as with the previously defined parameters directed path-width and directed cut-width. It turns out that the parameters directed linear clique-width, directed linear NLC-width, directed neighbourhood-width, and directed linear rank-width are equivalent in that sense, that all of these parameters can be upper bounded by each of the others. For the restriction to digraphs of bounded vertex degree directed path-width and directed cut-width are equivalent. Further for the restriction to semicomplete digraphs of bounded vertex degree all six mentioned width parameters are equivalent. We also show close relations of the measures to their undirected versions of the underlying undirected graphs, which allow us to show the hardness of computing the considered linear width parameters for directed graphs. Further we give first characterizations for directed graphs defined by parameters of small width.

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Section: Directed Path-widthmentioning

confidence: 99%

Comparing Linear Width Parameters for Directed Graphs

Gurski

Rehs

2019

Theory Comput Syst

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“…Further characterizations for transitive tournaments and thus for orientated co-graphs which are oriented cliques can be found in [Gou12, Chapter 9] and [GRR18].…”

Section: Oriented Threshold Graphsmentioning

confidence: 99%

“…Please note that transitive tournaments on n vertices are unique up to isomorphism, see [Gou12, Chapter 9] and[GRR18].…”

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confidence: 99%

Characterizations for Special Directed Co-graphs

Gurski

Komander

Rehs

2019

Lecture Notes in Computer Science

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Undirected co-graphs are those graphs which can be generated from the single vertex graph by disjoint union and join operations. Co-graphs are exactly the P4-free graphs (where P4 denotes the path on 4 vertices). Co-graphs itself and several subclasses haven been intensively studied. Among these are trivially perfect graphs, threshold graphs, weakly quasi threshold graphs, and simple co-graphs.Directed co-graphs are precisely those digraphs which can be defined from the single vertex graph by applying the disjoint union, order composition, and series composition. By omitting the series composition we obtain the subclass of oriented co-graphs which has been analyzed by Lawler in the 1970s and the restriction to linear expressions was recently studied by Boeckner. There are only a few versions of subclasses of directed co-graphs until now. By transmitting the restrictions of undirected subclasses to the directed classes, we define the corresponding subclasses for directed co-graphs. We consider directed and oriented versions of threshold graphs, simple co-graphs, co-simple co-graphs, trivially perfect graphs, co-trivially perfect graphs, weakly quasi threshold graphs and co-weakly quasi threshold graphs. For all these classes we provide characterizations by finite sets of minimal forbidden induced subdigraphs. Further we analyze relations between these graph classes.

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“…Please note that transitive tournaments on n vertices are unique up to isomorphism (see Gould 2012, Chapter 9),Gurski et al (2018) and Lemma 5.…”

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confidence: 99%

On characterizations for subclasses of directed co-graphs

2020

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Undirected co-graphs are those graphs which can be generated from the single vertex graph by disjoint union and join operations. Co-graphs are exactly the $$P_4$$ P 4 -free graphs (where $$P_4$$ P 4 denotes the path on 4 vertices). The class of co-graphs itself and several subclasses haven been intensively studied. Among these are trivially perfect graphs, threshold graphs, weakly quasi threshold graphs, and simple co-graphs. Directed co-graphs are digraphs which can be defined by, starting with the single vertex graph, applying the disjoint union, order composition, and series composition. By omitting the series composition we obtain the subclass of oriented co-graphs which has been analyzed by Lawler in the 1970s. The restriction to linear expressions was recently studied by Boeckner. Until now, there are only a few versions of subclasses of directed co-graphs. By transmitting the restrictions of undirected subclasses to the directed classes, we define the corresponding subclasses for directed co-graphs. We consider directed and oriented versions of threshold graphs, simple co-graphs, co-simple co-graphs, trivially perfect graphs, co-trivially perfect graphs, weakly quasi threshold graphs and co-weakly quasi threshold graphs. For all these classes we give characterizations by finite sets of minimal forbidden induced subdigraphs. Additionally, we analyze the relations between these graph classes.

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Directed Path-Width of Sequence Digraphs

Cited by 4 publications

References 22 publications

Comparing Linear Width Parameters for Directed Graphs

Comparing Linear Width Parameters for Directed Graphs

Characterizations for Special Directed Co-graphs

On characterizations for subclasses of directed co-graphs

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