Décompositions acircuituques de grands graphes orientés:
des apsects algorithmiques aux aspects combinatoires.

Abstract : This Thesis deals with structural properties of oriented graph.
We investigate algorithm and combinatorial properties of three different colourings: oriented, mixed and circuit-free decomposition.
For the oriented colouring, we obtain inapproximability results and, for particular cases, NP-complete classes.
To overcome these difficulties, we introduce the notion of mixed colouring and we get a differential approximation result and an
interpretation of mixed chromatic polynomial that generalizes Stanley's result for some mixed graphs. By relaxing the independent
set monochromatic class constraint, we investigate the complexity of circuit-free decomposition, we characterize a family of critical
indecomposable tournaments and we establish the primary properties of the circuit-free chromatic polynomial.
Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00134814
Contributor : Jean-François Culus <>
Submitted on : Monday, March 5, 2007 - 2:38:19 PM
Last modification on : Wednesday, May 23, 2018 - 5:58:05 PM
Long-term archiving on : Wednesday, April 7, 2010 - 1:23:30 AM

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  • HAL Id : tel-00134814, version 1

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Jean-François Culus. Décompositions acircuituques de grands graphes orientés:
des apsects algorithmiques aux aspects combinatoires.. Mathématiques [math]. Université Toulouse le Mirail - Toulouse II, 2006. Français. ⟨tel-00134814⟩

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