rank width
- 2023/02 Torunczyk2023
- inf-flip-width $k$ upper bounds rank width by $\mathcal O(k)$ – For every graph $G$, we have $\mathrm{rankwidth}(G) \le 3 \mathrm{fw}_\infty(G)+1 …
- rank width $k$ upper bounds inf-flip-width by $2^{\mathcal O(k)}$ – For every graph $G$, we have … $3 \mathrm{fw}_\infty(G)+1 \le O(2^{\mathrm{rankwidth(G)}}).
- 2012 GanianTwinCover2012
- page 263 : twin-cover number $k$ upper bounds rank width by $\mathcal O(k)$ – The rank-width and linaer rank-width of graph of twin-cover $k$ are at most $k+1$.
- 2011 BuiXuan2011
- boolean width $k$ upper bounds rank width by $2^{\mathcal O(k)}$ – \textbf{Corollary 1.} For any graph $G$ and decomposition tree $(T,\gamma)$ of $G$ it holds that … $\log_2 rw(G) \le boolw(G)$ …
- rank width $k$ upper bounds boolean width by $k^{\mathcal O(1)}$ – \textbf{Corollary 1.} For any graph $G$ and decomposition tree $(T,\gamma)$ of $G$ it holds that … $boolw(G) \le \frac 14 rw^2(G)+O(rw(G))$.
- 2006 Oum2006
- rank width $k$ implies that clique width is $2^{\mathcal O(k)}$ – Proposition 6.3
- clique width $k$ upper bounds rank width by $\mathcal O(k)$ – Proposition 6.3
- unknown
- linear rank width $k$ upper bounds rank width by $f(k)$
- branch width $k$ upper bounds rank width by $\mathcal O(k)$
- https://www.sciencedirect.com/science/article/pii/S0095895605001528
- rank width – see Section 6