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Graphclass: (2K2,C5)-free

Complement classes:  (C4,C5)-free 
See also: 2K2 C5

Inclusions

Minimal superclasses:  2K2-free   (C5,P5)-free   hole-free   odd-hole-free   perfect connected-dominant 
Maximal subclasses:  (1,1)-colorable   (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(K1,4),co-(X85))-free   (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(X85))-free   (2K2,C4,C5,S3,net)-free   (2K2,C4,C5)-free   (2K2,C5,S3,X159,X160,X161,X162,X46,X70,co-(2P3),co-(3K2),co-(H),co-(P2 cup P4),co-(X1),co-rising sun,house,net)-free   (2K2,C5,co-(C6),co-(C7),co-(C8),co-claw,co-diamond)-free   (2K2,C5,co-(T2))-free   (2K2,P4)-free   (2K2,co-(C6),odd anti-cycle)-free   2K2-free cap probe trivially perfect   (S3,net)-free cap split   co-(Cn+4)-free   (co-(T3),co-(X81),co-cycle)-free   absolutely perfect   chordal cap co-chordal   co-chordal   co-cycle-free   co-interval cap cograph   co-trivially perfect   probe co-trivially perfect cap probe trivially perfect   probe threshold   split 

Problems summary

Recognition:Polynomialdetails
Cliquewidth expression: Unbounded or NP-complete details
Cliquewidth:Unboundeddetails
Weighted independent set:Polynomialdetails
Independent set:Polynomialdetails
Domination:NP-completedetails

Algorithms for Recognition

Polynomial
     Finite forbidden subgraph characterization


Algorithms for Cliquewidth expression

See also : Cliquewidth : Weighted independent set : Domination

Algorithms for Cliquewidth


Unbounded from (2K2,co-(C6),odd anti-cycle)-free 
     From the complement .

Unbounded from (2K2,C5,co-(C6),co-(C7),co-(C8),co-claw,co-diamond)-free 
     From the complement .




Unbounded from (co-(Cn+4),co-XF2n+1,co-XF3n,co-claw)-free 
     From the complement .




Unbounded from split  [1176]
Unbounded from (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(X85))-free 
     From the complement .

Unbounded from (S3,co-(Cn+4),co-claw,net)-free 
     From the complement .






Unbounded from (co-(Cn+4),co-claw)-free 
     From the complement .

Unbounded from (S3,co-(Cn+4),co-claw)-free 
     From the complement .





Unbounded from (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(K1,4),co-(X85))-free 
     From the complement .











Unbounded from (S3,co-(Cn+4),co-(S3 cup K1),co-claw)-free 
     From the complement .






Unbounded from (co-(Cn+4),co-(H))-free 
     From the complement .



Unbounded from co-interval 
     See  interval  .


See also : Cliquewidth expression

Algorithms for Weighted independent set

Polynomial from nK2-free, fixed n  [1102]
Polynomial from K2 cup claw-free  [1290]
Polynomial from (P5,X82,X83)-free  [1246]
Polynomial from 2K2-free  [1160]
See also : Cliquewidth expression : Independent set

Algorithms for Independent set

See also : Weighted independent set

Algorithms for Domination

NP-complete from split  [1144] [1145]
See also : Cliquewidth expression