linear rank-width

• unknown source
  • linear rank-width upper bounds rank-width by a computable function
  • pathwidth upper bounds linear rank-width by a computable function
• Adler2015
  • page 1 : linear rank-width upper bounds linear clique-width by a computable function – 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 upper bounds linear rank-width by a computable function – 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 upper bounds linear rank-width by a linear function – Lemma 5. Any graph $G$ satisfies $\mathrm{lrw}(G) \le \mathrm{pw}(G)$.
• GanianTwinCover2012
  • page 263 : twin-cover number upper bounds linear rank-width by a linear function – The rank-width and linaer rank-width of graph of twin-cover $k$ are at most $k+1$.