Massively Winning Configurations in the Convex Grabbing Game on the Plane
Abstract
The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large oddsized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large evensized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.11247
 arXiv:
 arXiv:2106.11247
 Bibcode:
 2021arXiv210611247D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Metric Geometry
 EPrint:
 A slightly shorter version was published in CCCG 2021 (the 33rd Canadian Conference on Computational Geometry). Reason for update: improved illustrations