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Graphclass: (2K3,2P3,C5,C6,C7,K2,3,K3 cup P3,X84,co-(3K2),co-(C4 cup P2),co-(C6),co-(P2 cup P4),co-(P6),co-(X18),co-(X5),co-antenna,co-domino,co-fish)-free

References: [1254]
Equivalent classes:  (1,2)-polar 
Complement classes:  (3K2,C4 cup P2,C5,C6,K2 cup K3,K3,3,K3,3+e,P2 cup P4,P6,X18,X5,co-(2P3),co-(C6),co-(C7),co-(X84),antenna,domino,fish)-free 
See also: X84 co-domino co-(C6) 2P3 co-(X5) co-(X18) co-(P2 cup P4) co-antenna co-(P6) co-(C4 cup P2) 2K3 co-(3K2) C7 C6 C5 K3 cup P3 co-fish K2,3

Inclusions

Minimal superclasses:  (1,2)-colorable   2-split cap perfect   (C6,co-(C6))-free   K2,3-free   P4-bipartite   P7-free   (anti-hole,hole)-free   odd-hole-free   polar   weakly chordal 
Maximal subclasses:  (1,1)-colorable   (1,2)-polar cap chordal   (2K2,C4,C5,S3,net)-free   (2K2,C4,C5)-free   (2K3,2P3,C4,K3 cup P3,P4)-free   (2K3,2P3,Cn+4,K3 cup P3)-free   (S3,net)-free cap split   chordal cap co-chordal   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 split  [1176]
See also : Cliquewidth expression

Algorithms for Weighted independent set

Polynomial [O(n^{6p+2})] from (p,q<=2)-colorable  [1116]
Polynomial from perfect  [476]
Polynomial [O(V^4)] from weakly chordal  [997]
See also : Cliquewidth expression : Independent set

Algorithms for Independent set

Polynomial [O(VE)] from weakly chordal  [530] [1119]
See also : Weighted independent set

Algorithms for Domination

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