Journal of Combinatorial Theory Series B
Graph classes: a survey
On graph powers for leaf-labeled trees
Journal of Algorithms
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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
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
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A graph G is the k-leaf power of a tree T if its vertices are leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most k. Then T is the k-leaf root of G. This notion was introduced and studied by Nishimura, Ragde, and Thilikos motivated by the search for underlying phylogenetic trees. Their results imply a O(n3) time recognition algorithm for 3-leaf powers. Later, Dora, Guo, Hüffner, and Niedermeier characterized 3-leaf powers as the (bull, dart, gem)-free chordal graphs. We show that a connected graph is a 3-leaf power if and only if it results from substituting cliques into the vertices of a tree. This characterization is much simpler than the previous characterizations via critical cliques and forbidden induced subgraphs and also leads to linear time recognition of these graphs.