Abstract.
We extend the well-studied concept of a graph power to that of a k-leaf power G of a tree T: G is formed by creating a node for each leaf in the tree and an edge between a pair of nodes if and only if the associated leaves are connected by a path of length at most k. By discovering hidden combinatorial structure of cliques and neighbourhoods, we have developed polynomial-time algorithms that, for k = 3 and k = 4, identify whether or not a given graph G is a k-leaf power of a tree T, and if so, produce a tree T for which G is a k-leaf power. We believe that our structural results will form the basis of a solution for more general k. The general problem of inferring hidden tree structure on the basis of leaf relationships shows up in several areas of application.
Research supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Communications and Information Technology Ontario (CITO).
Research supported by the Ministry of Education and Culture of Spain, Grant number MEC-DGES SB98 0K148809.
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Nishimura, N., Ragde, P., Thilikos, D.M. (2000). On Graph Powers for Leaf-Labeled Trees. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_12
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DOI: https://doi.org/10.1007/3-540-44985-X_12
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