Combinatorial Analysis of a Subtraction Game on Graphs
Abstract
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then it would also be deleted. A player wins the game when the other player has no moves available. We study this game under various viewpoints: by finding specific strategies for certain families of graphs, through using properties of a graph's automorphism group, by writing a program to look at Sprague-Grundy numbers, and by studying the game when played on random graphs. When analyzing Grim played on paths, using the Sprague-Grundy function, we find a connection to a standing open question about Octal games.
Cite
@article{arxiv.1507.05673,
title = {Combinatorial Analysis of a Subtraction Game on Graphs},
author = {Richard Adams and Janae Dixon and Jennifer Elder and Jamie Peabody and Oscar Vega and Karen Willis},
journal= {arXiv preprint arXiv:1507.05673},
year = {2016}
}
Comments
13 pages, 0 figures