Weird claim of graphclasses about complexity of domination EDIT this got 'fixed' on graphclasses, as per answers/comments, so you might not reproduce it, unless you have their earlier database, which is publicly available via sage - http://sagemath.org.



Likely this is technical error in graphclasses or in me.

Appears to me graphclasses claims P=NP.

In Domination perfect
we have $\gamma(G)=i(G)$ which implies the complexity of Dominating Set
 (DS) and Independent Dominating Set (IDS) is the same in subclasses of
domination perfect.

In line graphs
we have DS NP-complete and IDS Polynomial.

According to the java application of graphclasses, line graphs
are domination perfect, one of the reasons is they are claw-free.

Appears to me this implies P=NP.


  What is wrong?


Screenshot:





Answering vb le question about polynomial IDS on line.

Clicking details recursively, we get: Polynomial on claw-free 
and the claim without reference on claw-free:


  Polynomial On domination perfect graphs, the Independent set and Independent domininating set problems are equivalent.
The culprit is the claim that Weighted-IDS is polynomial on claw-free graphs, because the independent set problem is and for domination perfect graphs, IDS is equivalent to IS. But for domination perfect graphs, IDS is not equivalent to IS, but to dominating set. So the statement should be: IDS is NPC on line graphs, because domination is.