2012/07/29 by Parikshit Kolipaka, Kolipaka, Parikshit, Sathish Govindarajan +1 · 1 citation
Business, Management and Accounting · Mathematics · #Computational Geometry (cs.CG) #Consumer Market Behavior and Pricing #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Point processes and geometric inequalities
paper · doi:10.48550/arxiv.1207.6778
openalex publication_date 2012/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.