Notes on the combinatorial game: Graph Nim

Richard M. LOW, Wai Hong CHAN

Research output: Contribution to journalArticles

Abstract

The combinatorial game of Nim can be played on graphs. Over the years, various Nim-like games on graphs have been proposed and studied by N.J. Calkin et al., L.A. Erickson and M. Fukuyama. In this paper, we focus on the version of Nim played on graphs which was introduced by N.J. Calkin et al.: Two players alternate turns, each time choosing a vertex v of a finite graph and removing any number (≥ 1) of edges incident to v. The player who cannot make a move loses the game. Here, we analyze Graph Nim for various classes of graphs and also compute some Grundy-values. Copyright © 2016 Bandung Indonesian Combinatorial Society.
Original languageEnglish
Pages (from-to)190-205
JournalElectronic Journal of Graph Theory and Applications
Volume4
Issue number2
DOIs
Publication statusPublished - 2016

Citation

Low, R. M., Chan, W. H. (2016). Notes on the combinatorial game: Graph Nim. Electronic Journal of Graph Theory and Applications, 4(2), 190-205.

Keywords

  • Nim on graphs
  • Combinatorial game

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