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Graphclass: (3K2,E,P2 cup P4,net)-free

Equivalent classes:  co-hereditary clique-Helly 
Complement classes:  (S3,co-(3K2),co-(E),co-(P2 cup P4))-free   hereditary clique-Helly   hereditary maximal clique irreducible 
See also: P2 cup P4 net E 3K2

Inclusions

Minimal superclasses:  E-free   P7-free 
Maximal subclasses:  1-bounded tripartite   (2C4,3K2,C6,E,P2 cup P4,P6,X25,X26,X27,X28,X29,odd-cycle)-free   (2K2,C4,C5,S3,net)-free   (2K2,P4)-free   (3K2,C4 cup P2,C5,P2 cup P4,P5,S3,X1,X46,X70,co-(3K2),co-(C4 cup P2),co-(P2 cup P4),co-(X1),co-(X46),co-(X70),co-fish,co-rising sun,fish,house,net,rising sun)-free   (3K2,co-(P),co-gem,house)-free   Dilworth 2   (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   (S3,net)-free cap split   (XC1,XC2,XC3,XC4,XC5,XC6,XC7,XC8)-free   (XC7,co-(XC1),co-(XC2),co-(XC3),co-(XC4),co-(XC5),co-(XC6),co-(XC8))-free   (co-(Cn+4),net)-free   (co-(W4),co-claw,co-gem)-free   (co-(W4),co-gem)-free   bipartite cap bithreshold   (co-diamond,diamond)-free   co-interval cap cograph   co-trivially perfect   strict 2-threshold   threshold signed 

Problems summary

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

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-diamond)-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 (co-(W4),co-claw,co-gem)-free 
     From the complement .

Unbounded from co-bipartite 
     See  bipartite  .

Unbounded from (2K2,co-(C6),odd anti-cycle)-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 (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 (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 (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 (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-(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

See also : Cliquewidth expression : Independent set

Algorithms for Independent set

Polynomial from co-hereditary clique-Helly  [1298]
See also : Weighted independent set

Algorithms for Domination

See also : Cliquewidth expression