A branch decomposition of a graph $G$ is a pair $(T,\chi)$, where $T$ is a binary tree and $\chi$ is a bijection, mapping leaves of $T$ to edges of $G$. Any edge $\{u, v\}$ of the tree divides the tree into two components and divides the set of edges of $G$ into two parts $X, E \backslash X$, consisting of edges mapped to the leaves of each component. The width of the edge $\{u,v\}$ is the number of vertices of $G$ that is incident both with an edge in $X$ and with an edge in $E \backslash X$. The width of the decomposition $(T,\chi)$ is the maximum width of its edges. The branchwidth of the graph $G$ is the minimum width over all branch-decompositions of $G$.
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
[?]
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FPT | [+]Details |