Reduced component max-leaf is a new graph parameter strictly between clique-width and reduced bandwidth that unifies tractability results and implies bounded treewidth under bounded degree in sparse classes.
Geometric and combinatorial structures on graphs.PhD thesis, Technical University of Berlin, Dec 2007
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Moderately beyond clique-width: reduced component max-leaf and related parameters
Reduced component max-leaf is a new graph parameter strictly between clique-width and reduced bandwidth that unifies tractability results and implies bounded treewidth under bounded degree in sparse classes.