Linearity Is Strictly More Powerful Than Contiguity for Encoding Graphs

  • Christophe CrespelleEmail author
  • Tien-Nam Le
  • Kevin Perrot
  • Thi Ha Duong Phan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)


Linearity and contiguity are two parameters devoted to graph encoding. Linearity is a generalisation of contiguity in the sense that every encoding achieving contiguity k induces an encoding achieving linearity k, both encoding having size \(\Theta (k.n)\), where n is the number of vertices of G. In this paper, we prove that linearity is a strictly more powerful encoding than contiguity, i.e. there exists some graph family such that the linearity is asymptotically negligible in front of the contiguity. We prove this by answering an open question asking for the worst case linearity of a cograph on n vertices: we provide an \(O(\log n/\log \log n)\) upper bound which matches the previously known lower bound.


Rooted Tree Interval Graph Tight Bound Arbitrary Graph Factorial Rank 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Christophe Crespelle
    • 1
    • 2
    • 6
    Email author
  • Tien-Nam Le
    • 3
  • Kevin Perrot
    • 4
    • 5
  • Thi Ha Duong Phan
    • 6
  1. 1.Université Claude Bernard Lyon 1VilleurbanneFrance
  2. 2.CNRS, DANTE/INRIA, LIP UMR CNRS 5668ENS de Lyon, Université de LyonLyonFrance
  3. 3.ENS de Lyon, Université de LyonLyonFrance
  4. 4.DIM, CMM UMR CNRS 2807Universidad de ChileSantiagoChile
  5. 5.CNRS, LIF UMR 7279Aix-Marseille UniversitéMarseilleFrance
  6. 6.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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