Cleaning Random d-Regular Graphs with Brushes Using a Degree-Greedy Algorithm

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. Key words: cleaning process, random d-regular graphs, degree–greedy algorithm, differential equations method

• Type: Conference
• Year: 2007
• Where: CAAN
• Authors: Margaret-Ellen Messinger, Pawel Pralat, Richard J. Nowakowski, Nicholas C. Wormald
• Keywords: CAAN 2007, Degree-greedy Algorithm, Discrete Geometry, Differential Equations Method, Random D-regular Graphs