Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a complexity theoretic classification of homomorphism problems for graphs and, more generally, relational structures obtained by restricting the left hand side structure in a homomorphism. For every class C of structures, let HOM(C, /spl I.bar/) be the problem of deciding whether a given structure A /spl isin/ C has a homomorphism to a given (arbitrary) structure B.  prove that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C, /spl I.bar/) is in polynomial time if, and only if, the cores of all structures in C have bounded tree-width (as long as the structures in C only contain relations of bounded arity). Due to a ll known correspondence beten homomorphism problems and constraint satisfaction problems, our classification carries over to the latter.
['Martin Grohe']
I am writing a research paper on a idea The complexity of homomorphism and constraint satisfaction problems seen from the other side
[{"from": "human", "value": "I am writing a research paper on a idea The complexity of homomorphism and constraint satisfaction problems seen from the other side"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a complexity theoretic classification of homomorphism problems for graphs and, more generally, relational structures obtained by restricting the left hand side structure in a homomorphism. For every class C of structures, let HOM(C, /spl I.bar/) be the problem of deciding whether a given structure A /spl isin/ C has a homomorphism to a given (arbitrary) structure B.  prove that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C, /spl I.bar/) is in polynomial time if, and only if, the cores of all structures in C have bounded tree-width (as long as the structures in C only contain relations of bounded arity). Due to a ll known correspondence beten homomorphism problems and constraint satisfaction problems, our classification carries over to the latter."}]