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Article

The Clique-Width of Minimal Series-Parallel Digraphs

by
Frank Gurski
1,* and
Ruzayn Quaddoura
2
1
Institute of Computer Science, Heinrich Heine University, 40225 Dusseldorf, Germany
2
Department of Computer Science, Zarqa University, Zarqa 13110, Jordan
*
Author to whom correspondence should be addressed.
Algorithms 2025, 18(6), 323; https://doi.org/10.3390/a18060323
Submission received: 28 March 2025 / Revised: 22 May 2025 / Accepted: 27 May 2025 / Published: 28 May 2025
(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

Abstract

MSP DAGs (short for minimal series-parallel digraphs) can be defined from the single vertex graph by applying the parallel composition and series composition. We prove an upper bound of 6 for the directed clique-width of MSP DAGs and show how a directed clique-width 6-expression can be found in linear time. Our 6-expression can be used to construct an MSP DAG G from its binary decomposition tree T(G) in linear time. We apply our bound on the directed clique-width to conclude a number of algorithmic consequences for MSP DAGs.
Keywords: directed clique-width; minimal series-parallel digraphs; digraphs directed clique-width; minimal series-parallel digraphs; digraphs

Share and Cite

MDPI and ACS Style

Gurski, F.; Quaddoura, R. The Clique-Width of Minimal Series-Parallel Digraphs. Algorithms 2025, 18, 323. https://doi.org/10.3390/a18060323

AMA Style

Gurski F, Quaddoura R. The Clique-Width of Minimal Series-Parallel Digraphs. Algorithms. 2025; 18(6):323. https://doi.org/10.3390/a18060323

Chicago/Turabian Style

Gurski, Frank, and Ruzayn Quaddoura. 2025. "The Clique-Width of Minimal Series-Parallel Digraphs" Algorithms 18, no. 6: 323. https://doi.org/10.3390/a18060323

APA Style

Gurski, F., & Quaddoura, R. (2025). The Clique-Width of Minimal Series-Parallel Digraphs. Algorithms, 18(6), 323. https://doi.org/10.3390/a18060323

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