Confusion danger: This class is sometimes called evenholefree .
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The map shows the inclusions between the current class and a fixed set of landmark classes. Minimal/maximal is with respect to the contents of ISGCI. Only references for direct inclusions are given. Where no reference is given, check equivalent classes or use the Java application. To check relations other than inclusion (e.g. disjointness) use the Java application, as well.
Problems in italics have no summary page and are only listed when ISGCI contains a result for the current class.
3Colourability
[?]

Unknown to ISGCI  [+]Details  
Clique
[?]

Polynomial  [+]Details  
Clique cover
[?]

Unknown to ISGCI  [+]Details  
Cliquewidth
[?]
Whether the cliquewidth of the graphs in this class is bounded by a
constant k
.
The cliquewidth of a graph is the number of different labels that is needed to construct the graph using the following operations:

Unbounded  [+]Details  
Cliquewidth expression
[?]

Unbounded or NPcomplete  [+]Details  
Colourability
[?]

Unknown to ISGCI  [+]Details  
Cutwidth
[?]

NPcomplete  [+]Details  
Domination
[?]

NPcomplete  [+]Details  
Feedback vertex set
[?]

Unknown to ISGCI  [+]Details  
Graph isomorphism
[?]

GIcomplete  [+]Details  
Hamiltonian cycle
[?]

NPcomplete  [+]Details  
Hamiltonian path
[?]

NPcomplete  [+]Details  
Independent dominating set
[?]

Unknown to ISGCI  [+]Details  
Independent set
[?]

Unknown to ISGCI  [+]Details  
Maximum cut
[?]
(decision variant)

NPcomplete  [+]Details  
Recognition
[?]

Polynomial  [+]Details  
Treewidth
[?]

Unknown to ISGCI  [+]Details  
Weighted clique
[?]

Polynomial  [+]Details  
Weighted feedback vertex set
[?]

Unknown to ISGCI  [+]Details  
Weighted independent dominating set
[?]

Unknown to ISGCI  [+]Details  
Weighted independent set
[?]

Unknown to ISGCI  [+]Details  
Weighted maximum cut
[?]
(decision variant)

NPcomplete  [+]Details 