Nim on the Complete Graph

Details Nim on the Complete Graph Nim on the Complete Graph

2010-10-07

arxiv.org/abs/1010.1455v1

Mathematics

Combinatorics

11 pages, 6 figures

Scientific paper

The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these results and introduce the strategy for even cycles. This paper examines a more general class of graphs by restricting the edge weight to one. We provide structural conditions for which there exist a winning strategy. This yields the solution for the complete graph.

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