Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The injective edge coloring number ź i ' ( G ) is the minimum number of colors permitted in a coloring of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then e1 and e3 receive the different colors. Let ω' denote the number of edges in a maximum clique of G. A graph G is called an ω' edge injective colorable (or perfect EIC-)graph if ź i ' ( G ) = ω ' . ,  give a sharp bound of the injective coloring number of a 2-connected graph with some forbidden conditions, and then  also characterize some perfect EIC-graph classes, which extends the results of perfect EIC-graph of Cardoso et al. in Injective edge chromatic index of a graph, http://arxiv.org/abs/1510.02626..
['Jun Yue', 'Shiliang Zhang', 'Xia Zhang']
I am writing a research paper on a idea Note on the perfect EIC-graphs
[{"from": "human", "value": "I am writing a research paper on a idea Note on the perfect EIC-graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The injective edge coloring number \u017a i ' ( G ) is the minimum number of colors permitted in a coloring of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then e1 and e3 receive the different colors. Let \u03c9' denote the number of edges in a maximum clique of G. A graph G is called an \u03c9' edge injective colorable (or perfect EIC-)graph if \u017a i ' ( G ) = \u03c9 ' . ,  give a sharp bound of the injective coloring number of a 2-connected graph with some forbidden conditions, and then  also characterize some perfect EIC-graph classes, which extends the results of perfect EIC-graph of Cardoso et al. in Injective edge chromatic index of a graph, http://arxiv.org/abs/1510.02626.."}]