page 1 : linear rank-width $k$ upper bounds linear clique-width by $f(k)$ – Linear rank-width is equivalent to linear clique-width in the sense that any graph class has bounded linear clique-width if and only if it has bounded linear rank-width.
page 1 : linear clique-width $k$ upper bounds linear rank-width by $f(k)$ – Linear rank-width is equivalent to linear clique-width in the sense that any graph class has bounded linear clique-width if and only if it has bounded linear rank-width.
page 3 : pathwidth $k$ upper bounds linear rank-width by $\mathcal O(k)$ – Lemma 5. Any graph $G$ satisfies $\mathrm{lrw}(G) \le \mathrm{pw}(G)$.
page 263 : twin-cover number $k$ upper bounds linear rank-width by $\mathcal O(k)$ – The rank-width and linaer rank-width of graph of twin-cover $k$ are at most $k+1$.