Article
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The Clique Width of Two Classes of Series-Parallel Digraphs
Version 1
: Received: 21 March 2024 / Approved: 25 March 2024 / Online: 26 March 2024 (03:16:55 CET)
How to cite: Quaddoura, R. The Clique Width of Two Classes of Series-Parallel Digraphs . Preprints 2024, 2024031498. https://doi.org/10.20944/preprints202403.1498.v1 Quaddoura, R. The Clique Width of Two Classes of Series-Parallel Digraphs . Preprints 2024, 2024031498. https://doi.org/10.20944/preprints202403.1498.v1
Abstract
The concept of graphs with clique-width at most was first introduced by Courcelle et al.to be the graphs that can be characterized using -expressions derived from graph operations that use labels of vertices. If the clique-width for some graph is bounded then a grand number of algorithmic problems, in general NP-hard, can be solved in polynomial time when restricted to this graph. This important fact motivated the researchers to prove that the clique-width of certain graphs is bounded. Following this research direction, we prove in this paper that the clique-width of series-parallel digraphs is at most 6 and we present an time algorithm to construct a 6-expression for this class of digraphs. In another part, we present a linear time recognition algorithm for a similar class of series-parallel digraphs and prove that the clique-width of this class is at most 3.
Keywords
Series parallel digraphs; Clique-width; Complexity
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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