Reconfiguration of Time-Respecting Arborescences

An arborescence, which is a directed analogue of spanning tree in an undirected graph, one the most fundamental combinatorial objects digraph. In this paper, we study arborescences digraphs from viewpoint reconfiguration, field where reachability between two configurations some via specified operations. Especially, consider reconfiguration problems for time-respecting arborescences, were introduced by Kempe, Kleinberg, and Kumar. We first prove that if roots initial target are same, then arborescence always reachable can find shortest sequence polynomial time. Furthermore, show not may be one. On other hand, determine whether form Finally, it NP-hard to case same. Our results interesting contrast previous (ordinary) problems.