Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A mixed hypergraph is a pair H = (V, E ∪ A), where V is the vertex set and E (A) the edge (the co-edge) set of H. A legal colouring of H gives the same (different) colour(s) to at least two vertices of any co-edge (of any edge). The upper chromatic number of H is the maximum number X(H) of colours that can be used in a legal colouring. After giving a general upper bound to X(H),  here consider the co-hypergraph J = (X,φ ∪ I), where I is a (v3,b2)- configuration I over X.  prove that computing X(J) is NP-hard, but there exists a polynomial-time algorithm returning a colouring with ≥ 5/6 X(J) colours.  also provide an example showing that this approximation factor is tight.
['Claudio Arbib', 'Michele Flammini']
I am writing a research paper on a idea On the upper chromatic number of ( v 3 ,b 2 )-configurations
[{"from": "human", "value": "I am writing a research paper on a idea On the upper chromatic number of ( v 3 ,b 2 )-configurations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A mixed hypergraph is a pair H = (V, E \u222a A), where V is the vertex set and E (A) the edge (the co-edge) set of H. A legal colouring of H gives the same (different) colour(s) to at least two vertices of any co-edge (of any edge). The upper chromatic number of H is the maximum number X(H) of colours that can be used in a legal colouring. After giving a general upper bound to X(H),  here consider the co-hypergraph J = (X,\u03c6 \u222a I), where I is a (v3,b2)- configuration I over X.  prove that computing X(J) is NP-hard, but there exists a polynomial-time algorithm returning a colouring with \u2265 5/6 X(J) colours.  also provide an example showing that this approximation factor is tight."}]