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Linear time construction of 5-phylogenetic roots for tree chordal graphs

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Abstract

Inspired by phylogenetic tree construction in computational biology, Lin et al. (The 11th Annual International Symposium on Algorithms and Computation (ISAAC 2000), pp. 539–551, 2000) introduced the notion of a k -phylogenetic root. A k-phylogenetic root of a graph G is a tree T such that the leaves of T are the vertices of G, two vertices are adjacent in G precisely if they are within distance k in T, and all non-leaf vertices of T have degree at least three. The k-phylogenetic root problem is to decide whether such a tree T exists for a given graph G. In addition to introducing this problem, Lin et al. designed linear time constructive algorithms for k≤4, while left the problem open for k≥5. In this paper, we partially fill this hole by giving a linear time constructive algorithm to decide whether a given tree chordal graph has a 5-phylogenetic root; this is the largest class of graphs known to have such a construction.

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Authors and Affiliations

  1. Discrete Mathematics Group, Department of Mathematics, McGill University, Montréal, Québec, H3A 2A7, Canada

    William S. Kennedy

  2. Academy of Mathematics and Systems Science, Zhongguancun, Beijing, 100080, China

    Hui Kong & Guiying Yan

  3. Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2E8, Canada

    Guohui Lin

Authors
  1. William S. Kennedy
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  2. Hui Kong
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  3. Guohui Lin
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  4. Guiying Yan
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Corresponding author

Correspondence to Guohui Lin.

Additional information

Research of W.S. Kennedy partially supported by NSERC.

Research of H. Kong partially supported by NNSF Grants 10721101 and 10531070.

Research of G. Lin partially supported by CFI and NSERC.

Research of G. Yan partially supported by NSERC and NNSF Grants 10721101 and 10531070.

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Kennedy, W.S., Kong, H., Lin, G. et al. Linear time construction of 5-phylogenetic roots for tree chordal graphs. J Comb Optim 19, 94–106 (2010). https://doi.org/10.1007/s10878-008-9164-y

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  • DOI: https://doi.org/10.1007/s10878-008-9164-y

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