Abstract
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every algorithmic problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ 1,L ) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time. The concept of clique-width extends the one of treewidth since bounded treewidth implies bounded clique-width.
We give a complete classification of all graph classes defined by forbidden one-vertex extensions of the P 4 with respect to their clique-width. Our results extend and improve recently published structural and complexity results in a systematic way.
Research of the first author partially supported by Kent State University, Kent, Ohio, research of the third and fourth author partially supported by German Research Community DFG Br 1446-4/1
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Brandstädt, A., Dragan, F.F., Le, HO., Mosca, R. (2002). New Graph Classes of Bounded Clique-Width. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_6
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DOI: https://doi.org/10.1007/3-540-36379-3_6
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