无向边地理博弈在堆叠棱柱图上的研究

中文摘要 AI 辅助

无向边地理博弈是一种在无向图上进行的双人组合博弈。玩家从根顶点开始，轮流沿一条关联边将根移动到其另一端点，然后删除该边。第一个没有剩余可走步的玩家为输家。对于正整数 $m$ 和 $n$，其中 $m\geq 3$，堆叠棱柱图定义为 $SP(m,n)=C_m\square P_n$。本文完全确定了 $m\geq 2$ 时 $SP(2m,n)$ 以及 $m\geq 3$ 时 $SP(m,2)$ 上的博弈赢家，并为赢家提供了获胜策略。

英文摘要

The undirected edge geography is a two-player combinatorial game on an undirected graph. The players start at the root vertex and alternately move the root along an incident edge to its other endpoint and then delete that edge. The first player who has no remaining move is the loser. For positive integers $m$ and $n$ where $m\geq 3$, the stacked prism graph is $SP(m,n)=C_m\square P_n$. In this paper, we completely determine the winner of the game on $SP(2m,n)$ for $m\geq 2$ and $SP(m,2)$ for $m\geq 3$, and provide a winning strategy for the winner.

发表机构

• Prince of Songkla University（宋卡王子大学）

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