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On Bichromatic Triangle Game

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Author(s):
Manic, Gordana ; Martin, Daniel M. ; Stojakovic, Milos
Total Authors: 3
Document type: Journal article
Source: DISCRETE APPLIED MATHEMATICS; v. 164, p. 6-pg., 2014-02-19.
Abstract

We study a combinatorial game called Bichromatic Triangle Game, defined as follows. Two players R and 2 construct a triangulation on a given planar point set V. Starting from no edges, they take turns drawing one straight edge that connects two points in V and does not cross any of the previously drawn edges. Player R uses color red and player 2 uses color blue. The first player who completes one empty monochromatic triangle is the winner. We show that each of the players can force a tie in the Bichromatic Triangle Game when the points of V are in convex position, and also in the case when there is exactly one inner point in the set V. As a consequence of those results, we obtain that the outcome of the Bichromatic Complete Triangulation Game (a modification of the Bichromatic Triangle Game) is also a tie for the same two cases regarding the set V. (C) 2012 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 08/06508-8 - Discrete optimization and graphs: algorithms, theory and applications
Grantee:Gordana Manic
Support Opportunities: Research Grants - Young Investigators Grants