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Graphclass: K2 cup claw-free

Complement classes:  co-(K2 cup claw)-free 
See also: K2 cup claw

Inclusions

Maximal subclasses:  1-bounded tripartite   2-bounded bipartite   (2K2,C4)-free   (2K2,P4)-free   2K2-free   (4K1,K4)-free   4K1-free   (A,C4 cup 2K1,P2 cup P3,R,co-(K5 - e),co-(W5),co-claw,twin-C5,twin-house)-free   (C5,C6 cup K1,C7,K3,3 cup K1,K3,3-e cup K1,co-(K5 - e),domino cup K1,triangle)-free   (C5,K2 cup K3,K2,3,P,P2 cup P3,P5,co-(P),co-(P2 cup P3),co-fork,fork,house)-free   C5-free cap matrogenic   (K3,3,K4,W4 cup K1,W5,X86,X87,X88,X89,X90,co-(C7),co-(X38),co-(X39),co-(butterfly cup K1),co-diamond)-free   (P2 cup P3,house)-free   XC9-free   (co-(K1,4),co-diamond)-free   co-(XC10)-free   co-(XC12)-free   claw-free   (co-diamond,diamond)-free   (co-diamond,odd anti-hole)-free   co-interval cap cograph   (co-paw,odd anti-hole)-free   (co-paw,paw)-free   co-trivially perfect   matrogenic   matroidal   pseudo-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 (S3,co-(Cn+4),co-(S3 cup K1),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 (2K2,co-diamond)-free 
     From the complement .



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

Unbounded from co-bipartite 
     See  bipartite  .















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





Unbounded from (2K2,co-(X91),co-claw)-free 
     From the complement .



Unbounded from co-comparability graphs of posets of interval dimension 2, height 1 
     See  comparability graphs of posets of interval dimension 2, height 1  .


Unbounded from (2K3,3K1,co-(A),co-(H),co-(X45))-free 
     From the complement .

Unbounded from (2K2,claw)-free  [1183]






Unbounded from (3K1,co-(T2),co-(X2),co-(X3),anti-hole)-free 
     From the complement .


Unbounded from (2K2,4K1,co-claw,co-diamond)-free 
     From the complement .






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

Unbounded from (K2 cup K3,P5,co-(X37),co-(X38),co-diamond,co-domino,co-twin-C5)-free 
     From the complement .









Unbounded from (co-(XC11),co-claw,co-diamond)-free 
     From the complement .

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



Unbounded from co-interval 
     See  interval  .




Unbounded from unit interval  [1177]


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



Unbounded from (A,C4 cup 2K1,P2 cup P3,R,co-(K5 - e),co-(W5),co-claw,twin-C5,twin-house)-free 
     From the complement .


Unbounded from (3K1,co-(H))-free 
     From the complement .



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


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









Unbounded from (co-claw,co-diamond)-free 
     From the complement .

Unbounded from (C4,K4,claw,diamond)-free  [1183]

Unbounded from (co-(K1,4),co-diamond)-free 
     From the complement .

Unbounded from co-(XC12)-free 
     From the complement .

Unbounded from (3K1,co-cross)-free 
     From the complement .


Unbounded from co-(XC10)-free 
     From the complement .


Unbounded from split  [1176]
Unbounded from Fn grid  [1176]

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








Unbounded from (K2 cup K3,co-diamond)-free 
     From the complement .




See also : Cliquewidth expression

Algorithms for Weighted independent set

Polynomial [1290]
See also : Cliquewidth expression : Independent set

Algorithms for Independent set

See also : Weighted independent set

Algorithms for Domination

NP-complete from line  [1129]
NP-complete from split  [1144] [1145]
See also : Cliquewidth expression