The cutwidth of a graph $G$ is the smallest integer $k$ such that the vertices of $G$ can be arranged in a linear layout $v_1, \ldots, v_n$ in such a way that for every $i = 1, \ldots,n - 1$, there are at most $k$ edges with one endpoint in $\{v_1, \ldots, v_i\}$ and the other in ${v_{i+1}, \ldots, v_n\}$.
Minimal/maximal is with respect to the contents of ISGCI. Only references for direct bounds are given. Where no reference is given, check equivalent parameters.
Problems in italics have no summary page and are only listed when ISGCI contains a result for the current parameter.
3-Colourability
[?]
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FPT | [+]Details | |||||
Clique
[?]
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FPT | [+]Details | |||||
Clique cover
[?]
|
XP | [+]Details | |||||
Colourability
[?]
|
FPT | [+]Details | |||||
Domination
[?]
|
FPT | [+]Details | |||||
Feedback vertex set
[?]
|
FPT | [+]Details | |||||
Graph isomorphism
[?]
|
FPT | [+]Details | |||||
Hamiltonian cycle
[?]
|
FPT | [+]Details | |||||
Hamiltonian path
[?]
|
FPT | [+]Details | |||||
Independent set
[?]
|
FPT | [+]Details | |||||
Maximum cut
[?]
(decision variant)
|
FPT | [+]Details | |||||
Monopolarity
[?]
|
Unknown to ISGCI | [+]Details | |||||
Polarity
[?]
|
XP | [+]Details | |||||
Weighted clique
[?]
|
FPT | [+]Details | |||||
Weighted feedback vertex set
[?]
|
FPT | [+]Details | |||||
Weighted independent dominating set
[?]
|
FPT | [+]Details | |||||
Weighted independent set
[?]
|
FPT | [+]Details |