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A strategy for Isolator in the Toucher-Isolator game on trees
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- In the Toucher-Isolator game, introduced recently by Dowden, Kang, Mikala\v{c}ki and Stojakovi\'{c}, Toucher and Isolator alternately claim an edge from a graph such that Toucher aims to touch as many vertices as possible, while Isolator aims to isolate as many vertices as possible, where Toucher plays first. Among trees with $n$ vertices, they showed that the star is the best choice for Isolator and they asked for the most suitable tree for Toucher. Later, R\"{a}ty showed that the answer is the path with $n$ vertices. We give a simple alternative proof of this result. The method to determine where Isolator should play is by breaking down the gains and losses in each move of both players.<br />Comment: 11 pages, 3 figures, 3 tables, submitted
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9d4406114da2bc89bfabffd7dd39d199
- Full Text :
- https://doi.org/10.48550/arxiv.2005.01931