Massively winning configurations in the convex grabbing game on the plane
Dvorak, Martin
Nicholson, Sara
convex grabbing game
graph grabbing game
combinatorial game
convex geometry
ddc:516
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 odd-sized 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 even-sized 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.
CCCG
2021
info:eu-repo/semantics/conferenceObject
doc-type:conferenceObject
text
http://purl.org/coar/resource_type/c_5794
https://research-explorer.ista.ac.at/record/9592
https://research-explorer.ista.ac.at/download/9592/9616
https://research-explorer.ista.ac.at/download/9592/9902
Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. In: <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>. CCCG; 2021.
eng
info:eu-repo/semantics/altIdentifier/arxiv/2106.11247
info:eu-repo/semantics/openAccess