Bounded Degree Closest k-Tree Power Is NP-Complete
An undirected graph G=(V,E) is the k-power of an undirected tree T=(V,E′) if (u,v)∈ E iff u and v are connected by a path of length at most k in T. The tree T is called the tree root of G. Tree powers can be recognized in polynomial time. The thus naturally arising question is whether a graph G can be modified by adding or deleting a specified number of edges such that G becomes a tree power. This problem becomes NP-complete for k≥ 2. Strengthening this result, we answer the main open question of Tsukiji and Chen [COCOON 2004] by showing that the problem remains NP-complete when additionally demanding that the tree roots must have bounded degree.
KeywordsVertex Cover Chordal Graph Edge Node Tree Power Induce Subgraph
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