A tree depth decomposition of a graph $G = (V,E)$ is a rooted tree $T$ with the same vertices $V$, such that, for every edge $\{u,v\} \in E$, either $u$ is an ancestor of $v$ or $v$ is an ancestor of $u$ in the tree $T$. The depth of $T$ is the maximum number of vertices on a path from the root to any leaf. The tree depth of a graph $G$ is the minimum depth among all tree depth decompositions.
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
[?]
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XP | [+]Details | |||||
Colourability
[?]
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FPT | [+]Details | |||||
Domination
[?]
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FPT | [+]Details | |||||
Feedback vertex set
[?]
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FPT | [+]Details | |||||
Graph isomorphism
[?]
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FPT | [+]Details | |||||
Hamiltonian cycle
[?]
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FPT | [+]Details | |||||
Hamiltonian path
[?]
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FPT | [+]Details | |||||
Independent set
[?]
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FPT | [+]Details | |||||
Maximum cut
[?]
(decision variant)
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FPT | [+]Details | |||||
Monopolarity
[?]
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Unknown to ISGCI | [+]Details | |||||
Polarity
[?]
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XP | [+]Details | |||||
Weighted clique
[?]
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FPT | [+]Details | |||||
Weighted feedback vertex set
[?]
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FPT | [+]Details | |||||
Weighted independent dominating set
[?]
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FPT | [+]Details | |||||
Weighted independent set
[?]
|
FPT | [+]Details |