Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A digraph is $k$-traceable if its order is at least $k$ and each of its subdigraphs of order $k$ is traceable.  The Traceability Conjecture (TC) states that for $k\geq 2$ every $k$-traceable oriented graph of order at least $2k-1$ is traceable. It has been shown that for $2\leq k\leq 6$, every $k$-traceable oriented graph is traceable.  develop an iterative procedure to extend previous results regarding the TC. In particular,  prove that every $7$-traceable oriented graph of order at least 9 is traceable and every 8-traceable graph of order at least 14 is traceable.
['Susan A. van Aardt', 'Alewyn P. Burger', 'Jean E. Dunbar', 'Marietjie Frick', 'John M. Harris', 'Joy Singleton']
I am writing a research paper on a idea An Iterative Approach to the Traceability Conjecture for Oriented Graphs
[{"from": "human", "value": "I am writing a research paper on a idea An Iterative Approach to the Traceability Conjecture for Oriented 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 digraph is $k$-traceable if its order is at least $k$ and each of its subdigraphs of order $k$ is traceable.\u00a0 The Traceability Conjecture (TC) states that for $k\\geq 2$ every $k$-traceable oriented graph of order at least $2k-1$ is traceable. It has been shown that for $2\\leq k\\leq 6$, every $k$-traceable oriented graph is traceable.  develop an iterative procedure to extend previous results regarding the TC. In particular,  prove that every $7$-traceable oriented graph of order at least 9 is traceable and every 8-traceable graph of order at least 14 is traceable."}]