Nim on the Complete Graph
Combinatorics
2010-10-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1010.1455,
title = {Nim on the Complete Graph},
author = {Lindsay Erickson},
journal= {arXiv preprint arXiv:1010.1455},
year = {2010}
}
Comments
11 pages, 6 figures