关于三角形的双色着色游戏

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Rairo-Operations Research Pub Date : 2023-09-01 DOI:10.1051/ro/2023162

Naoki Matsumoto

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引用次数: 0

摘要

本文研究了由Aichholzer等人于2005年提出的圆盘三角剖分上的双色着色游戏。他们证明，如果一个圆盘三角形最多有两个内部顶点，那么第二个玩家可以在圆盘三角形的双色着色游戏中强行打平。我们证明了相同的命题适用于任何至多有四个内顶点的圆盘三角剖分，并且内顶点的数目界是可能的最佳界。进一步，我们考虑了拓扑三角剖分上的博弈。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bichromatic coloring game on triangulations

In this paper, we study bichromatic coloring game on a disk triangulation, which is introduced by Aichholzer et al. in 2005. They proved that if a disk triangulation has at most two inner vertices, then the second player can force a tie in the bichromatic coloring game on the disk triangulation. We prove that the same statement holds for any disk triangulation with at most four inner vertices, and that the bound of the number of inner vertices is the best possible. Furthermore, we consider the game on topological triangulations.

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来源期刊

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.