Linear-Time Constant-Ratio Approximation Algorithm and Tight Bounds for the Contiguity of Cographs

  • Christophe Crespelle
  • Philippe Gambette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7748)


In this paper we consider a graph parameter called contiguity which aims at encoding a graph by a linear ordering of its vertices. We prove that the contiguity of cographs is unbounded but is always dominated by O(logn), where n is the number of vertices of the graph. And we prove that this bound is tight in the sense that there exists a family of cographs on n vertices whose contiguity is Ω(logn). In addition to these results on the worst-case contiguity of cographs, we design a linear-time constant-ratio approximation algorithm for computing the contiguity of an arbitrary cograph, which constitutes our main result. As a by-product of our proofs, we obtain a min-max theorem, which is worth of interest in itself, stating equality between the rank of a tree and the minimum height its path partitions.


Approximation Algorithm Induction Hypothesis Rooted Tree Interval Graph Neighborhood Query 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christophe Crespelle
    • 1
  • Philippe Gambette
    • 2
  1. 1.Université Claude Bernard Lyon 1, DNET/INRIA, LIP UMR CNRS 5668, ENS de Lyon, Université de LyonFrance
  2. 2.Université Paris-Est, LIGM UMR CNRS 8049, Université Paris-EstChamps-sur-MarneFrance

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