XP status of MAD Spanning Tree parameterized by cliquewidth

Ascertain whether the MAD Spanning Tree problem belongs to the class XP when parameterized by cliquewidth; specifically, determine whether there exists an algorithm that solves MADST on graphs of cliquewidth k in time |V(G)|^{f(k)} for some computable function f.

Background

While the paper establishes FPT for modular width and XP for treewidth, the status for cliquewidth remains unsettled. Earlier work raised the question of whether MADST is in XP for cliquewidth, and the authors explicitly reiterate that this is an open question.

Resolving XP for cliquewidth would extend the landscape of tractable structural parameters for MADST and connect it to a broader class of dense graph decompositions.