On the complexity of join dependencies
ACM Transactions on Database Systems (TODS)
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
Introduction to Algorithms
On graph powers for leaf-labeled trees
Journal of Algorithms
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
On k- Versus (k + 1)-Leaf Powers
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Closest 4-leaf power is fixed-parameter tractable
Discrete Applied Mathematics
The NLC-width and clique-width for powers of graphs of bounded tree-width
Discrete Applied Mathematics
Theoretical Computer Science
The complete inclusion structure of leaf power classes
Theoretical Computer Science
Characterising (k,l)-leaf powers
Discrete Applied Mathematics
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
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Ptolemaic graphs and interval graphs are leaf powers
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
5-th phylogenetic root construction for strictly chordal graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On relaxing the constraints in pairwise compatibility graphs
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Exploring pairwise compatibility graphs
Theoretical Computer Science
Hi-index | 0.00 |
A fundamental problem in computational biology is the phylogeny reconstruction for a set of specific organisms. One of the graph theoretical approaches is to construct a similarity graph on the set of organisms where adjacency indicates evolutionary closeness, and then to reconstruct a phylogeny by computing a tree interconnecting the organisms such that leaves in the tree are labeled by the organisms and every organism appears as a leaf in the tree. The similarity graph is simple and undirected. For any pair of adjacent organisms in the similarity graph, their distance in the output tree, which is measured by the number of edges on the path connecting them, must be less than some pre-specified bound. This is known as the problem of recognizing leaf powers and computing leaf roots. Graphs that are leaf powers are known to be chordal. It is shown in this paper that all strictly chordal graphs are leaf powers and a linear time algorithm is presented to compute a leaf root for any given strictly chordal graph. An intermediate root-and-power problem, the Steiner root problem, is also examined.