Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the recently introduced model for cleaning a graph with brushes,  use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even).  then use a differential equations method to find the (asymptotic) number of brushes needed to clean a random d-regular graph using this algorithm. As ll as the case for general d, interesting results for specific values of d are examined.  also state various open problems.
['Margaret-Ellen Messinger', 'Paweł Prałat', 'Richard J. Nowakowski', 'Nicholas C. Wormald']
I am writing a research paper on a idea Cleaning random d-regular graphs with brushes using a degree-greedy algorithm
[{"from": "human", "value": "I am writing a research paper on a idea Cleaning random d-regular graphs with brushes using a degree-greedy algorithm"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the recently introduced model for cleaning a graph with brushes,  use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even).  then use a differential equations method to find the (asymptotic) number of brushes needed to clean a random d-regular graph using this algorithm. As ll as the case for general d, interesting results for specific values of d are examined.  also state various open problems."}]