Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A 3-connected graph $G$ is akly 3-connected if, for every edge $e$ of $G$, at most one of $G\backslash e$ and $G/e$ is 3-connected. The main result of this paper is that any akly 3-connected graph can be reduced to $K_4$ by a sequence of simple operations. This extends a result of Das [5] on minimally 3-connected graphs.
['Donald K. Wagner']
I am writing a research paper on a idea Weakly 3-Connected Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Weakly 3-Connected Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A 3-connected graph $G$ is akly 3-connected if, for every edge $e$ of $G$, at most one of $G\\backslash e$ and $G/e$ is 3-connected. The main result of this paper is that any akly 3-connected graph can be reduced to $K_4$ by a sequence of simple operations. This extends a result of Das [5] on minimally 3-connected graphs."}]