Two player game variant of the Erdos-Szekeres problem

Kolipaka, Parikshit and Govindarajan, Sathish (2013) Two player game variant of the Erdos-Szekeres problem. In: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 15 (3). pp. 73-100.

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Abstract

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.

Item Type:	Journal Article
Publication:	DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
Publisher:	DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE
Additional Information:	Copy right for this article belongs to the DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE, 62 RUE DU CARDINAL MATHIEU, F-54000 NANCY, FRANCE
Keywords:	Erdos-Szekeres problem; Ramsey theory; convex k-gon; empty convex k-gon
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	26 Aug 2015 04:50
Last Modified:	26 Aug 2015 04:50
URI:	http://eprints.iisc.ac.in/id/eprint/52179

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