Sign games on graphs
Combinatorics
2025-11-12 v2
Abstract
We define the Sign Game as a two-player game played on a simple undirected mathematical graph . The players alternate turns, assigning vertices of either or , and edges take on the value of the product of their endvertices. The game ends when all vertices are assigned values, and the score of the game is the sum of all edge values. One player's goal is to make the score positive while the other's is to make the score negative. In this paper we investigate the game being played on various types of graphs, determining outcomes and winning strategies.
Cite
@article{arxiv.2511.05451,
title = {Sign games on graphs},
author = {Liz Blum and Lily Brustkern and Rosetta Hawkins and Neil R. Nicholson and Ranjan Rohatgi},
journal= {arXiv preprint arXiv:2511.05451},
year = {2025}
}
Comments
15 pages, 5 figures