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Graphclass: frame hereditary dominating pair

Definition:
Three vertices of a graph form an asteroidal triple if every two of them are connected by a path avoiding the neighbourhood of the third.
A graph G is frame hereditary dominating pair (frame HDP) if it is a  dominating pair  graph with an asteroidal triple T such that all vertices of G are on an induced path between two vertices of T that avoid the neighbourhood of the third vertex of T.

References: [1292]
Related classes:  AT-free   dominating pair 

Inclusions

Minimal superclasses:  C6-free   P7-free   dominating pair 

Problems summary

Recognition: Unknown to ISGCI details
Cliquewidth expression: Unknown to ISGCI details
Cliquewidth: Unknown to ISGCI details
Weighted independent set: Unknown to ISGCI details
Independent set: Unknown to ISGCI details
Domination: Unknown to ISGCI details

Algorithms for Recognition

Algorithms for Cliquewidth expression

See also : Cliquewidth : Weighted independent set : Domination

Algorithms for Cliquewidth

See also : Cliquewidth expression

Algorithms for Weighted independent set

See also : Cliquewidth expression : Independent set

Algorithms for Independent set

See also : Weighted independent set

Algorithms for Domination

See also : Cliquewidth expression