Let G = (V, E) be a simple undirected graph and $c ∈ Z^V$ weights on the nodes of G.
A vertex set C ⊆ V is called Clique if {u, v} ∈ E holds for all u, v ∈ C, with u not equal to v.
A node set S ⊆ V is called stable set if {u, v} doesn't belong to E holds for all u, v ∈ S, with u not equal to v.
Max-Weight-Clique Given: Graph $G = (V, E), c ∈ Z^V$ Find: a c-maximizing clique C ⊆ V
Max-Weight-Stable-Set Given: Graph $G = (V, E), c ∈ Z^V$ Find: a c-maximizing stable set S ⊆ V
Does anyone know how to prove the problem Max-Weight-Clique is polynomial reducible to Max-Weight-Stable-Set and vice versa?
I can't find any references, proofs or anything, so I am not even sure where to start or how such a proof would go,