Hamiltonian problems in directed graphs with simple row patterns

We define a row pattern of a matrix as a model (or a condition) to be satisfied by each row of the matrix, independently of the other rows. When applied to adjacency matrices of digraphs, a row pattern allows to define a class of digraphs characterized by a local condition on the out-neighborhood of...

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Veröffentlicht in:Theoretical computer science Jg. 916; S. 70 - 85
1. Verfasser: Rusu, Irena
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 19.05.2022
Elsevier
Schlagworte:
Complexity of algorithms
Computational Complexity
Computer Science
Consecutive ones property
Data Structures and Algorithms
Hamiltonian problems
Linear ordering of the vertices
Hamiltonian problems
Consecutive ones property
Complexity of algorithms
Linear ordering of the vertices
ISSN:0304-3975, 1879-2294
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Beschreibung
Zusammenfassung:We define a row pattern of a matrix as a model (or a condition) to be satisfied by each row of the matrix, independently of the other rows. When applied to adjacency matrices of digraphs, a row pattern allows to define a class of digraphs characterized by a local condition on the out-neighborhood of each vertex, once an appropriate linear ordering of the vertices has been found. We show that the Hamiltonian Cycle and Hamiltonian Path problems are NP-complete on digraphs with simple row patterns, namely C1P-digraphs (where the row pattern describes the consecutive ones property), 2-out-regular digraphs (where each row contains exactly two values 1) and sym-digraphs (where the 1s in each row are symmetric with respect to the main diagonal, as soon as the row contains at least two 1s). Classes with simple row patterns thus show a real structural complexity, despite their simple definitions. Moreover, they raise interesting class recognition problems.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.03.005