Under ETH, Max Cut has no n^{2^{o(k)}} f(k) algorithm on multi-clique-width k graphs while Hamiltonian Cycle and Edge Dominating Set admit n^{O(k)} algorithms, showing differing tight bounds from clique-width.
Circuits and Backdoors: Five Shades of the SETH
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Tight Bounds for some W[1]-hard Problems Parameterized by Multi-clique-width
Under ETH, Max Cut has no n^{2^{o(k)}} f(k) algorithm on multi-clique-width k graphs while Hamiltonian Cycle and Edge Dominating Set admit n^{O(k)} algorithms, showing differing tight bounds from clique-width.