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- W2040593601 abstract "It is well known that the clique-width of chordal gem-free graphs (also known as ptolemaic graphs), as a subclass of distance-hereditary graphs, is at most 3. Hereby, the gem consists of a P4 plus a vertex being completely adjacent to the P4, and the co-gem is its complement graph. On the other hand, unit interval graphs being another important subclass of chordal graphs, have unbounded clique-width. In this note, we show that, based on certain tree structure and module properties, chordal co-gem-free graphs have clique-width at most eight. By a structure result for (P5,gem)-free graphs, this implies bounded clique-width for this class as well. Moreover, known results on unbounded clique-width of certain grids and of split graphs imply that the gem and the co-gem are the only one-vertex P4 extension H such that chordal H-free graphs have bounded clique-width." @default.
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- W2040593601 date "2005-01-01" @default.
- W2040593601 modified "2023-09-27" @default.
- W2040593601 title "Chordal co-gem-free and (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif overflow=scroll><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math>,gem)-free graphs have bounded clique-width" @default.
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- W2040593601 doi "https://doi.org/10.1016/j.dam.2004.01.014" @default.
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