ACM Transactions on Algorithms (TALG)
Closest 4-leaf power is fixed-parameter tractable
Discrete Applied Mathematics
A good characterization of squares of strongly chordal split graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
Linear-Time algorithms for tree root problems
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Bounded degree closest k-tree power is NP-complete
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Computing square roots of trivially perfect and threshold graphs
Discrete Applied Mathematics
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In this paper, we study the complexity of recognizing powers of chordal graphs and its subclasses. We present the first polynomial time algorithm to recognize squares of proper interval graphs and give an outline of an algorithm to recognize kth powers of proper interval graphs for every natural number k. These are the first results of this type for a family of graphs that contains arbitrarily large cliques. On the other hand, we show the NP-completeness of recognizing squares of chordal graphs, recognizing squares of split graphs, and recognizing chordal graphs that are squares of some graph.