On graph powers for leaf-labeled trees

Naomi Nishimura, Prabhakar Ragde, Dimitrios M. Thilikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 discov-ering 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.

Original languageEnglish (US)
Title of host publicationAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
EditorsMagnús M. Halldórsson
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3540676902, 9783540676904
StatePublished - 2000
Event7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
Duration: Jul 5 2000Jul 7 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other7th Scandinavian Workshop on Algorithm Theory, SWAT 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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