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Graphclass: (3K1,co-cross)-free

Complement classes:  (cross,triangle)-free 
See also: co-cross 3K1

Inclusions

Minimal superclasses:  4K1-free   AT-free cap claw-free   (Cn+6,X37,claw,co-antenna,net,sun)-free   (P5,bull)-free   (P5,claw)-free   (co-(W4),co-(W5),co-butterfly)-free   (co-(W4),co-gem)-free   (bull,fork)-free 
Maximal subclasses:  (2K2,3K1,C5,co-(C6),co-(C7),co-(C8),co-(H),co-(K1,4),co-(X85))-free   (3K1,C5,K5 - e,co-(C6 cup K1),co-(C7),co-(K3,3 cup K1),co-(K3,3-e cup K1),co-(domino cup K1))-free   (3K1,co-fork)-free   (co-fork,odd anti-cycle)-free 

Problems summary

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

Algorithms for Recognition

Polynomial
     Finite forbidden subgraph characterization


Algorithms for Cliquewidth expression

See also : Cliquewidth : Weighted independent set : Domination

Algorithms for Cliquewidth



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

Unbounded
     From the complement .




See also : Cliquewidth expression

Algorithms for Weighted independent set

Linear from AT-free cap claw-free  [1157]
Polynomial [O(VE)] from (P5,fork)-free  [1125]
Polynomial [O(n^5)] from (K1,4,P5)-free  [1110]
Polynomial from (K2,3,P5)-free  [1110]
Polynomial from (P5,cricket)-free  [1110]
Polynomial from (P,P5)-free  [1353]
Polynomial from K2 cup claw-free  [1290]
Polynomial [O(VE)] from co-gem-free 
     Because for all v: G[\co{N}(v)] is P_4-free

Polynomial from fork-free  [1099]
Polynomial [O(n^6)] from (K3,3,P5)-free 
     Algorithm for (P_5,K_{m,m})-free (fixed m) [1118]

Polynomial [O(n^4)] from AT-free  [160]
Polynomial [O(n^8)] from (K4,4,P5)-free 
     Algorithm for (P_5,K_{m,m})-free (fixed m) [1118]

Polynomial from 4K1-free 
Polynomial from (K1,4,P,P5,fork)-free  [1103]
Polynomial [O(n^4)] from (P5,claw)-free  [1110]
Polynomial from claw-free  [783]
Polynomial from (P5,X82,X83)-free  [1246]
Polynomial [O(VE)] from (bull,fork)-free  [1124] [307]
Polynomial from (K2,3,P,P5)-free  [1107]
See also : Cliquewidth expression : Independent set

Algorithms for Independent set

Polynomial from claw-free  [947]
Polynomial from co-hereditary clique-Helly  [1298]
Polynomial from (K3,3-e,P5)-free  [1246]
Polynomial [O(VE)] from (P,P5)-free  [1117]
Polynomial from (E,P)-free  [1305]
Polynomial from (K2,3,P,P5)-free  [1346] [1107]
Polynomial [O(V^8)] from (P,P7)-free  [1351]
Polynomial from (C6,K3,3+e,P,P7,X37,X41)-free  [1346]
Polynomial [O(VE)] from (claw,net)-free  [1127] [515]
Polynomial from (P,T2)-free  [1305]
Polynomial [O(nm)] from (K3,3-e,P5,X98)-free  [1117]
Polynomial from (P,star1,2,5)-free  [1349]
Polynomial [O(V^{5})] from (K3,3-e,P5,X99)-free  [1307]
Polynomial from (P,P8)-free  [1306]
Open from (P,star1,2,3)-free  [1351]
Open from (P,star1,2,4)-free  [1351] [1306]
See also : Weighted independent set

Algorithms for Domination

Polynomial from AT-free  [1152]
Polynomial [O(VE)] from (claw,net)-free  [1127]
See also : Cliquewidth expression