Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The set ${\cal R}$ of relevant cycles of a graph $G$ is the union of its minimum cycle bases.  introduce a partition of ${\cal R}$ such that each cycle in a class ${\cal W}$ can be expressed as a sum of other cycles in ${\cal W}$ and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class ${\cal W}$. This result is used to derive upper and lor bounds on the number of distinct minimum cycle bases. Finally,  give a polynomial-time algorithm to compute this partition.
['Petra M. Gleiss', 'Josef Leydold', 'Peter F. Stadler']
I am writing a research paper on a idea Interchangeability of Relevant Cycles in Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Interchangeability of Relevant Cycles in Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The set ${\\cal R}$ of relevant cycles of a graph $G$ is the union of its minimum cycle bases.  introduce a partition of ${\\cal R}$ such that each cycle in a class ${\\cal W}$ can be expressed as a sum of other cycles in ${\\cal W}$ and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class ${\\cal W}$. This result is used to derive upper and lor bounds on the number of distinct minimum cycle bases. Finally,  give a polynomial-time algorithm to compute this partition."}]