Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study backbone colorings, a variation on classical vertex colorings: Given a graph G = (V, E) and a spanning subgraph H (the backbone) of G, a backbone coloring for G and H is a proper vertex coloring V → {1,2,...} in which the colors assigned to adjacent vertices in H differ by at least two.  concentrate on the cases where the backbone is either a spanning tree or a spanning path. For tree backbones of G, the number of colors needed for a backbone coloring of G can roughly differ by a multiplicative factor of at most 2 from the chromatic number X(G); for path backbones this factor is roughly 3/2. In the special case of split graphs G, the difference from X(G) is at most an additive constant 2 or 1, for tree backbones and path backbones, respectively. The computational complexity of the problem 'Given a graph G, a spanning tree T of G, and an integer  , is there a backbone coloring for G and T with at most   colors?' jumps from polynomial to NP-complete beten   = 4 (easy for all spanning trees) and   = 5 (difficult even for spanning paths).
['Hajo Broersma', 'Fedor V. Fomin', 'Petr A. Golovach', 'Gerhard J. Woeginger']
I am writing a research paper on a idea Backbone colorings for networks
[{"from": "human", "value": "I am writing a research paper on a idea Backbone colorings for networks"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study backbone colorings, a variation on classical vertex colorings: Given a graph G = (V, E) and a spanning subgraph H (the backbone) of G, a backbone coloring for G and H is a proper vertex coloring V \u2192 {1,2,...} in which the colors assigned to adjacent vertices in H differ by at least two.  concentrate on the cases where the backbone is either a spanning tree or a spanning path. For tree backbones of G, the number of colors needed for a backbone coloring of G can roughly differ by a multiplicative factor of at most 2 from the chromatic number X(G); for path backbones this factor is roughly 3/2. In the special case of split graphs G, the difference from X(G) is at most an additive constant 2 or 1, for tree backbones and path backbones, respectively. The computational complexity of the problem 'Given a graph G, a spanning tree T of G, and an integer  , is there a backbone coloring for G and T with at most   colors?' jumps from polynomial to NP-complete beten   = 4 (easy for all spanning trees) and   = 5 (difficult even for spanning paths)."}]