地理、科茨希的尼姆和变体

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2024-11-06 DOI:10.1016/j.tcs.2024.114957

Srinivas Arun

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引用次数: 0

摘要

地理学是一种组合游戏，在游戏中，两名玩家轮流沿着有向图的边移动一个标记，并删除它们所来自的顶点。福克斯和盖斯勒对给定图的各种地理变体中确定胜者的计算复杂度进行了分类，我们在此基础上对他们的工作进行了扩展。特别是，我们证明了在双向图上自由删除的无向偏态地理学和在无环图上自由删除的有向偏态地理学的 NP-hardness。此外，我们还研究了 Kotzig's Nim，这是地理学的一种特例，其中顶点是有标签的，移动对应于固定数量的添加。我们部分地解决了 Tan 和 Ward 关于具有特定移动集的博弈的猜想。

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Geography, Kotzig's Nim, and variants

Geography is a combinatorial game in which two players take turns moving a token along edges of a directed graph and deleting the vertex they came from. We expand upon work by Fox and Geissler, who classified the computational complexity of determining the winner of various Geography variants given a graph. In particular, we show NP-hardness for undirected partizan Geography with free deletion on bipartite graphs and directed partizan Geography with free deletion on acyclic graphs. In addition, we study Kotzig's Nim, a special case of Geography where the vertices are labeled and moves correspond to additions by fixed amounts. We partially resolve a conjecture by Tan and Ward about games with a certain move set.

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.