NP-hard problems in hierarchical-tree clustering
Acta Informatica
Computing roots of graphs is hard
Discrete Applied Mathematics
Algorithms for Square Roots of Graphs
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Graph classes: a survey
On graph powers for leaf-labeled trees
Journal of Algorithms
Recognizing Powers of Proper Interval, Split, and Chordal Graphs
SIAM Journal on Discrete Mathematics
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Computing bounded-degree phylogenetic roots of disconnected graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Closest 4-leaf power is fixed-parameter tractable
Discrete Applied Mathematics
On generating multivariate Poisson data in management science applications
Applied Stochastic Models in Business and Industry
Hi-index | 0.00 |
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.