(Nearly-)Tight Bounds on the Linearity and Contiguity of Cographs - Archive ouverte HAL Access content directly
Conference Papers Year :

(Nearly-)Tight Bounds on the Linearity and Contiguity of Cographs

Abstract

In this paper we show that the contiguity and linearity of cographs on n vertices are both O(log n). Moreover, we show that this bound is tight for contiguity as there exists a family of cographs on n vertices whose contiguity is Omega(log n). We also provide an Omega(log n / log log n) lower bound on the maximum linearity of cographs on n vertices. 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 of one of its path partitions.
Fichier principal
Vignette du fichier
2012CrespelleGambetteBGW.pdf (175.64 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00730247 , version 1 (08-09-2012)

Identifiers

  • HAL Id : hal-00730247 , version 1

Cite

Christophe Crespelle, Philippe Gambette. (Nearly-)Tight Bounds on the Linearity and Contiguity of Cographs. Bordeaux Graph Workshop, Nov 2012, France. pp.2. ⟨hal-00730247⟩
213 View
75 Download

Share

Gmail Facebook Twitter LinkedIn More