AI 中文总结
研究子图重新配置问题，证明了重配置特定图类为NP难，还将问题扩展到资源聚焦设置，探讨将不可重配置实例变为可重配置所需的额外缓冲区空间，给出了不同图类所需空间的结论。
AI 中文摘要
子图重新配置问题是指一个子图能否通过一系列局部变化转化为另一个子图，同时保持特定的图属性。本文聚焦于由边集指定子图的情况。贡献有两方面：一是受路径重配置为NP难而树重配置可线性求解的对比启发，证明了两个推广结论，包括对固定k≥1，重配置路径宽度至多为k的连通图是NP难等；二是将问题扩展到资源聚焦设置，研究将不可重配置实例变为可重配置所需的额外缓冲区空间，得出平面图等需要Ω(n)额外空间，仙人掌图在受限设置下O(1)空间就足够。
英文摘要
The subgraph reconfiguration problem asks whether one subgraph can be transformed into another via a sequence of local changes while maintaining a specified graph property. In this work, we focus on the setting where the subgraph is specified by its set of edges. Our contributions in this paper are twofold. First, motivated by the contrast that path reconfiguration is $\textsf{NP}$-hard while tree reconfiguration is solvable in linear time, we prove two generalizations: (1) for any fixed $k$ at least one, reconfiguring connected graphs with pathwidth at most $k$ is $\textsf{NP}$-hard, and (2) for any fixed $k$ at least two, reconfiguring graphs with pathwidth at most $k$ is also $\textsf{NP}$-hard. En route to proving (2), we show a general hardness result that applies to a range of minor-closed graph classes, which we use to show planar graph reconfiguration is also $\textsf{NP}$-hard. Second, given our negative results, we extend the problem to a resource-focused setting, asking how much additional buffer space is needed to turn a non-reconfigurable instance into a reconfigurable one. We show that $Ω(n)$ extra buffer space is needed for planar graphs and graphs with bounded pathwidth and treewidth, while $O(1)$ extra buffer space is sufficient for cactus graphs in a restricted setting.
