arXiv:1010.1455 Abstract | arXiv Analytics

arXiv:1010.1455 [math.CO]Abstract References Reviews Resources

Nim on the Complete Graph

Published 2010-10-07Version 1

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.

Comments: 11 pages, 6 figures

Categories: math.CO

Subjects: 05C57, G.2.2

Keywords: complete graph, structural conditions, edge weight, masahiko fukuyama, general class

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