超图及其他相关几何和离散结构上的可带走公平组合博弈
Take-Away Impartial Combinatorial Games on Hypergraphs and Other Related Geometric and Discrete Structures
摘要：
在超图的拿走游戏中，两个玩家轮流移除超图的顶点和超边。在每个回合中，玩家必须移除一个顶点或一个超边。当玩家选择移除一个顶点时，包含所选顶点的所有超边也会被移除。当一个玩家选择移除一个超边时，只有那个被选择的超边会被移除。去掉最后一个顶点的人赢得比赛。在仅奇一致超图和仅等一致超图上的带离公平组合对策的获胜策略的基础上，本文研究了非奇一致超图和非等一致超图上带离公平组合对策的新的获胜策略。然而，这些既不是奇一致超图，也不是完全一致超图，必须满足特定的给定要求。
英文摘要：
In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either a single vertex or a hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed. When a player chooses to remove one hyperedge, only that chosen hyperedge is removed. Whoever removes the last vertex wins the game. Following from the winning strategy for the Take-Away Impartial Combinatorial Games on only Oddly Uniform or only Evenly Uniform Hypergraphs, this paper is about the new winning strategy for Take-Away Games on neither Oddly nor Evenly Uniform Hypergraphs. These neither Oddly nor Evenly Uniform Hypergraphs, however, have to satisfy the specific given requirements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
