Abstract
In the recently introduced model for cleaning a graph with brushes, we use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even). We 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 well as the case for general d, interesting results for specific values of d are examined. We also state various open problems.
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Messinger, ME., Prałat, P., Nowakowski, R.J., Wormald, N. (2007). Cleaning Random d-Regular Graphs with Brushes Using a Degree-Greedy Algorithm. In: Janssen, J., Prałat, P. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2007. Lecture Notes in Computer Science, vol 4852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77294-1_4
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DOI: https://doi.org/10.1007/978-3-540-77294-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77293-4
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