COCOON 2005: Computing and Combinatorics pp 757-766

# Bounded Degree Closest k-Tree Power Is NP-Complete

• Michael Dom
• Jiong Guo
• Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3595)

## Abstract

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.

## Keywords

Vertex Cover Chordal Graph Edge Node Tree Power Induce Subgraph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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