Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph G is R-role assignable if there is a locally surjective homomorphism from G to R, i.e. a vertex mapping r: VG → VR, such that the neighborhood relation is preserved: r(NG(u)) = NR(r(u)). Kristiansen and Telle conjectured that the decision problem whether such a mapping exists is an NP-complete problem for any connected graph R on at least three vertices.   prove this conjecture, i.e.  give a complete complexity classification of the role assignment problem for connected graphs.  show further corollaries for disconnected graphs and related problems.
['Jir ´ i Fiala', 'Daniël Paulusma']
I am writing a research paper on a idea The computational complexity of the role assignment problem
[{"from": "human", "value": "I am writing a research paper on a idea The computational complexity of the role assignment problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph G is R-role assignable if there is a locally surjective homomorphism from G to R, i.e. a vertex mapping r: VG \u2192 VR, such that the neighborhood relation is preserved: r(NG(u)) = NR(r(u)). Kristiansen and Telle conjectured that the decision problem whether such a mapping exists is an NP-complete problem for any connected graph R on at least three vertices.   prove this conjecture, i.e.  give a complete complexity classification of the role assignment problem for connected graphs.  show further corollaries for disconnected graphs and related problems."}]