Journal of Combinatorial Theory Series B
SIAM Journal on Algebraic and Discrete Methods
Neighborhood subtree tolerance graphs
Discrete Applied Mathematics
Graph classes: a survey
Consecutive retrieval property-revisited
Information Processing Letters
On graph powers for leaf-labeled trees
Journal of Algorithms
Strictly chordal graphs are leaf powers
Journal of Discrete Algorithms
Structure and linear time recognition of 3-leaf powers
Information Processing Letters
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
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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
Characterising (k,l)-leaf powers
Discrete Applied Mathematics
On pairwise compatibility graphs having Dilworth number two
Theoretical Computer Science
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Motivated by the problem of reconstructing evolutionary history, Nishimura, Radge and Thilikos introduced the notion of k-leaf powers as the class of graphs G = (V, E) which have a k-leaf root, i.e., a tree T with leaf set V where xy ∈ E if and only if the T-distance between x and y is at most k. It is known that leaf powers are strongly chordal (i.e., sun-free chordal) graphs. Despite extensive research, the problem of recognizing leaf powers, i.e., to decide for a given graph G whether it is a k-leaf power for some k, remains open. Much less is known on the complexity of finding the leaf rank of G, i.e., to determine the minimum number k such that G is a k-leaf power. A result by Bibelnieks and Dearing implies that not every strongly chordal graph is a leaf power. Recently, Kennedy, Lin and Yan have shown that dart- and gem-free chordal graphs are 4-leaf powers. We generalize their result and show that ptolemaic (i.e., gem-free chordal) graphs are leaf powers. Moreover, ptolemaic graphs have unbounded leaf rank. Furthermore, we show that interval graphs are leaf powers which implies that leaf powers have unbounded clique-width. Finally, we characterize unit interval graphs as those leaf powers having a caterpillar leaf root.