Coloring powers of planar graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computing Phylogenetic Roots with Bounded Degrees and Errors
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Phylogenetic k-Root and Steiner k-Root
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing bounded-degree phylogenetic roots of disconnected graphs
Journal of Algorithms
ACM Transactions on Algorithms (TALG)
Radiocoloring in planar graphs: complexity and approximations
Theoretical Computer Science - Mathematical foundations of computer science 2000
Computing phylogenetic roots with bounded degrees and errors is NP-complete
Theoretical Computer Science - Computing and combinatorics
Strictly chordal graphs are leaf powers
Journal of Discrete Algorithms
Structure and linear-time recognition of 4-leaf powers
ACM Transactions on Algorithms (TALG)
Closest 4-leaf power is fixed-parameter tractable
Discrete Applied Mathematics
Complexity of the Packing Coloring Problem for Trees
Graph-Theoretic Concepts in Computer Science
The NLC-width and clique-width for powers of graphs of bounded tree-width
Discrete Applied Mathematics
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
Computing bounded-degree phylogenetic roots of disconnected graphs
Journal of Algorithms
The clique-width of tree-power and leaf-power graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Theoretical Computer Science
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
5-th phylogenetic root construction for strictly chordal graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Extending the tractability border for closest leaf powers
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On the approximability of the L(h, k)-labelling problem on bipartite graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Elegant distance constrained labelings of trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Computing bounded-degree phylogenetic roots of disconnected graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Distance three labelings of trees
Discrete Applied Mathematics
Hamiltonian paths in the square of a tree
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Computing square roots of trivially perfect and threshold graphs
Discrete Applied Mathematics
Square roots of minor closed graph classes
Discrete Applied Mathematics
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The $n$th power ($n \geq 1$) of a graph $G = (V, E)$, written $G^n$, is defined to be the graph having $V$ as its vertex set with two vertices $u, v$ adjacent in $G^n$ if and only if there exists a path of length at most $n$ between them. Similarly, graph $H$ has an $n$th root $G$ if $G^n = H$. For the case of $n = 2$, we say that $G^2$ is the square of $G$ and $G$ is the square root of $G^2$. This paper presents a linear time algorithm for finding the tree square roots of a given graph and a linear time algorithm for finding the square roots of planar graphs. A polynomial time algorithm for finding the square roots of subdivision graphs, which is equivalent to the problem of the inversion of total graphs, is also presented. Further, the authors give a linear time algorithm for finding a Hamiltonian cycle in a cubic graph and prove the NP-completeness of finding the maximum cliques in powers of graphs and the chordality of powers of trees.