WALCOM 2013: WALCOM: Algorithms and Computation pp 126-136

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

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

## Abstract

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.

## Keywords

Approximation Algorithm Induction Hypothesis Rooted Tree Interval Graph Neighborhood Query
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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