Resumen

LOPEZ-MEDINA, Marco Antonio; GONZALEZ-RUIZ, J. Leonardo; MARCIAL-ROMERO, J.Raymundo  y  HERNANDEZ, J. A.. Computing the Clique-Width on Series-Parallel Graphs. Comp. y Sist. [online]. 2022, vol.26, n.2, pp.815-822.  Epub 10-Mar-2023. ISSN 2007-9737.  https://doi.org/10.13053/cys-26-2-4250.

The clique-width $\left(cwd\right)$ is an invariant of graphs which, similar to other invariants like the tree-width $\left(twd\right)$ establishes a parameter for the complexity of a problem. For example, several problems with bounded clique-width can be solved in polynomial time. There is a well known relation between tree-width and clique-width denoted as $cwd\left(G\right)\le 3\cdot 2^{twd\left(G\right)-1}$. Serial-parallel graphs have tree-width of at most 2, so its clique–width is at most 6 according to the previous relation. In this paper, we improve the bound for this particular case, showing that the clique-width of series-parallel graphs is smaller or equal to 5.

Palabras llave : Graph theory; clique-width; tree-width; complexity; series-parallel.

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