两个滑动令牌的独立集重构所需移动次数的线性上界
A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens
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中文总结 AI 辅助
该研究针对图上两个滑动令牌的独立集重构问题，解答了相关学者提出的问题，证明其移动次数存在4n的线性上界。
中文摘要 AI 辅助
我们考虑在n个顶点的图G中，将放置在非相邻顶点u、v上的两个令牌，通过一系列令牌移动操作，移至G的两个非相邻顶点u'、v'的问题。每一步中，一个令牌从当前顶点移至其相邻顶点，且移动后令牌需保持非相邻状态。我们解答了Briański、Felsner、Hodor和Micek在《区间图上的独立集重构》（MFCS 2021）中提出的问题，证明若两个令牌可从初始位置移至目标位置，则最多仅需4n次移动即可完成。
英文摘要
We consider the problem of shifting two tokens placed on nonadjacent vertices $u,v$ of a graph $G$ on $n$ vertices to two nonadjacent vertices $u',v'$ of $G$ using a sequence of token movements. In each step, a token is moved from the vertex it is on to a neighbour of that vertex, ensuring that the tokens remain on nonadjacent vertices after this move. We answer a question of Briański, Felsner, Hodor, and Micek [``Reconfiguring Independent Sets on Interval Graphs'', MFCS 2021] by showing that if the two tokens can be moved from their initial position to their final position, then it can be done using at most $4n$ moves.
