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Clique-width of graphs defined by one-vertex extensions

Michaël Rao 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Let G be a graph and u be a vertex of G . We consider the following operation: add a new vertex v such that v does not distinguish any two vertices which are not distinguished by u . We call this operation a one-vertex extension. Adding a true twin, a false twin or a pendant vertex are cases of one-vertex extensions. Here we are interested in graph classes defined by a subset of allowed one-vertex extension. Examples are trees, cographs and distance-hereditary graphs. We give a complete classification of theses classes with respect to their clique-width. We also introduce a new graph parameter called the modular-width, and we give a relation with the clique-width.
Keywords : Clique-width
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00808032
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Submitted on : Thursday, April 4, 2013 - 5:14:16 PM
Last modification on : Thursday, February 7, 2019 - 2:51:37 PM

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Michaël Rao. Clique-width of graphs defined by one-vertex extensions. Discrete Mathematics, Elsevier, 2008, 308, pp.6157-6165. ⟨10.1016/j.disc.2007.11.039⟩. ⟨lirmm-00808032⟩

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