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Graphclass: chordal cap dominating pair

References: [1211]
Equivalent classes:  (Cn+4,T2,XF2n+1)-free 
Complement classes:  (co-(Cn+4),co-(T2),co-XF2n+1)-free 
Related classes:  chordal   dominating pair 

Inclusions

Minimal superclasses:  (C4,C5,T2)-free   (Cn+4,T2,net)-free   chordal cap diametral path   dominating pair 
Maximal subclasses:  (2,0)-colorable cap chordal   (2K2,C4,C5,S3,net)-free   (2K2,C4,C5,co-sun)-free   (3K1,C4,C5)-free   AT-free cap chordal   (C4,P4,dart)-free   (C4,P4)-free   (C4,odd anti-cycle)-free   C4-free cap co-comparability   (Cn+4,S3 cup K1,claw,net)-free   (Cn+4,T2,X31,XF2n+1,XF3n)-free   (Cn+4,claw,net)-free   (S3,net)-free cap split   boxicity 1   chordal cap (claw,net)-free   chordal cap co-comparability   chordal cap cograph   chordal cap proper circular arc   cograph cap interval   comparability graphs of arborescence orders   intersection graph of nested intervals   interval   quasi-threshold   superfragile   trivially perfect 

Problems summary

Recognition:Polynomialdetails
Cliquewidth expression: Unbounded or NP-complete details
Cliquewidth:Unboundeddetails
Weighted independent set:Lineardetails
Independent set:Lineardetails
Domination: Unknown to ISGCI details

Algorithms for Recognition

Polynomial [1292]

Algorithms for Cliquewidth expression

See also : Cliquewidth : Weighted independent set : Domination

Algorithms for Cliquewidth

Unbounded from unit interval  [1177]
See also : Cliquewidth expression

Algorithms for Weighted independent set

Linear from chordal  [1166]
Polynomial from (C4,C5,T2)-free  [1108]
Polynomial from (K2,3,P,hole)-free  [1107]
Polynomial from interval filament  [1159]
Polynomial from perfect  [476]
Polynomial [O(V^4)] from weakly chordal  [997]
Polynomial from subtree overlap  [1123]
See also : Cliquewidth expression : Independent set

Algorithms for Independent set

Linear from chordal  [425] [931]
Polynomial from Gallai  [1081]
Polynomial [O(VE)] from weakly chordal  [530] [1119]
Polynomial from (P,T2)-free  [1305]
Polynomial from Meyniel  [169]
Polynomial from clique separable  [1081]
See also : Weighted independent set

Algorithms for Domination

See also : Cliquewidth expression