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
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Phylogenetic k-Root and Steiner k-Root
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Bounded degree closest k-tree power is NP-complete
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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The Phylogenetic kth Root Problem (PRk) is theproblem of finding a (phylogenetic) tree T from a given graph G=(V,E) such that (1) T has no degree-2 internal nodes, (2) the external nodes (i.e. leaves) of T are exactly the elements of V, and (3) (u, v) ∈ E if and only if the distance between u and v in tree T is at most k, where k is some fixed threshold k. Such a tree T, if exists, is called a phylogenetickth root of graph G. The computational complexity of PRk is open, except for k ≤ 4. Recently, Chen et al. investigated PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant. They presented a linear-time algorithm that determines if a given connectedG has such a phylogenetic kth root, and if so, demonstrates one. In this paper, we supplement their work by presenting a linear-time algorithm for disconnected graphs.