Abstract
Region against region and army against army, we chart and battle among the stars! This paper studies the combinatorial game Aggression using graph-theoretic models. We focus on how winning strategies depend on the structure of the game graph, with particular attention to star graphs, matchings, and their disjoint union. The results presented here come from research conducted under the guidance of Dr. Kristen Barnard during the summer of 2025. We begin by introducing the game, describing the rule set used, and explaining how maps can be represented as graphs. From there, we examine how adjacency, placement order, and tie-breaking rules influence gameplay. A central theme of this work is the advantage held by Player 1. Through direct proofs and case analysis, we show that Player 1 has a winning strategy on isolated vertices, path graphs, star graphs with any number of pendant vertices, and finally we prove that Player 1 has the winning strategy on the combined graph consisting of a star and a matching. These results show how Player 1 so often wins and illustrate how graph structure shapes strategy in Aggression.
Recommended Citation
Chambers, E. and Barnard, Kristen
(2026)
"Matching the Stars to a Game of Aggression,"
Electronic Proceedings of Undergraduate Mathematics Day: Vol. 9, Article 5.
Available at:
https://ecommons.udayton.edu/epumd/vol9/iss1/5