Adler2015

https://www.doi.org/10.1016/j.tcs.2015.04.021

@article{Adler2015,
author = {Isolde Adler and Mamadou Moustapha Kanté},
doi = {10.1016/j.tcs.2015.04.021},
issn = {0304-3975},
journaltitle = {Theoretical Computer Science},
pages = {87--98},
title = {Linear rank-width and linear clique-width of trees},
volume = {589},
year = {2015},
}

• 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 $\mathrm{lrw}(G) \le \mathrm{pw}(G)$.