Abstract
polish is a game based on the ‘Cleaning with Brushes’ model. It is a combinatorial game in the sense of Conway but can be seen as a graph searching or chip-firing problem as well. We consider only the impartial version and give a characterization of graphs with maximum degree two that are first player wins. We also show that the second player can win on the complete graph Kn provided n≥3 and the complete bipartite graph K2,n provided n≠1,3. We give the nim-values for all positions on paths, stars, and also the nim-values for complete bipartite graphs where every vertex needs at most 3 more brushes to fire.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
