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Colorations de graphes et applications

Jean-Sébastien Sereni 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : This thesis is comprised of three parts. In the first one,
a channel assignment problem posed by Alcatel is modelled
as a graph colouring problem: a graph is k-improperly
l-colourable if, given l colours,
every vertex can be assigned a colour such that each colour
class induces a subgraph of maximum degree at most k.
Several problems are studied: improper colouring (and improper choosability) of graphs with bounded density (including the case of graphs of given genus and girth), unit disk graphs (including random instances and inifinite set of points), and also weighted improper colouring of subgraphs of the triangular lattice.

In the second part, different kinds of colouring, for
which we obtain new results, are studied: 3-facial colourings of plane graphs, circular choosability, and various types of edge-colourings of cubic graphs, in particular by elements of Abelian groups, and Steiner triple systems.

In the last part, we focus on a rerouting problem, without
service interruption, in WDM networks. First, a new invariant is introduced so as to model this problem. As it turns out that this parameter is close to the pathwidth, we then present some new results we get concerning the relation between the pathwidth of a 2-connected outerplanar graph and the pathwidth of its dual.
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Submitted on : Friday, December 15, 2006 - 3:18:21 PM
Last modification on : Monday, October 12, 2020 - 10:30:12 AM
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  • HAL Id : tel-00120594, version 1



Jean-Sébastien Sereni. Colorations de graphes et applications. Modélisation et simulation. Université Nice Sophia Antipolis, 2006. Français. ⟨tel-00120594⟩



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