AI 中文总结
本文证明偏袒边地理游戏在最大度为3的二分无向图上是PSPACE完全的，并指出该归约也适用于棋子不能同顶点的变体。
AI 中文摘要
偏袒边地理游戏是一种在图上进行的双人游戏，其中每个玩家在顶点上拥有自己的棋子，并在回合中将棋子移动到相邻顶点并移除该边。两名玩家轮流移动棋子，首先无法移动的玩家输掉游戏。Fraenkel 和 Simonson（TCS，1993）表明，在给定图和棋子位置的情况下，该游戏在无向图上的胜者判定是 PSPACE 完全的。本文通过证明在最大度为 3 的二分无向图上 PSPACE 完全性，解决了其在无向图上的复杂性。相同的归约也适用于两个棋子不能放置在同一个顶点的变体。
英文摘要
Partizan Edge Geography is a two-player game on a graph where each player has their own token on a vertex and moves their token to a neighbor in a turn removing the edge. Two player alternately move their tokens and the first player who cannot move loses the game. Fraenkel and Simonson (TCS, 1993) showed that the winner determination of this game is PSPACE-complete on directed graphs, given a graph and token positions. This paper resolves its complexity on undirected graphs by showing the PSPACE-completeness on bipartite undirected graphs of maximum degree 3. The same reduction also works for a variant where two tokens cannot be placed on the same vertex.
Comments9 pages, 6 figures
