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.
Node multiway cut and subset feedback vertex set on graphs of bounded mim-width.Algorithmica, 84(5):1385–1417
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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.