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Colorations de graphes sous contraintes

Abstract : In this thesis, we are interested in various coloring of graphs under constraints. We study acyclic coloring, strong edge coloring and adjacent vertex-distinguishing edge coloring.In Chapter 2, we consider acyclic coloring and we bound the acyclic chromatic number by a function of the maximum degree of the graph. We also study acyclic list coloring. The notion of acyclic list coloring of planar graphs was introduced by Borodin, Fon-Der Flaass, Kostochka, Raspaud, and Sopena. They conjectured that every planar graph is acyclically 5-choosable. We obtain some sufficient conditions for planar graphs to be acyclically 3-choosable.In Chapter 3, we study strong edge coloring of graphs. We prove some upper bounds of the strong chromatic index of subcubic graphs as a function of the maximum average degree. We also obtain a tight upper bound for the minimum number of colors in a strong edge coloring of outerplanar graphs as a function of the maximum degree. We also prove that the strong edge k-colouring problem, when k=4,5,6, is NP-complete for subcubic planar bipartite graphs with some girth condition. Finally, in Chapter 4, we focus on adjacent vertex-distinguishing edge coloring, or avd-coloring, of graphs. We bound the avd-chromatic number of graphs by a function of the maximum average degree. This work completes a result of Wang and Wang in 2010.
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Contributor : Hervé Hocquard Connect in order to contact the contributor
Submitted on : Tuesday, May 6, 2014 - 4:11:46 PM
Last modification on : Saturday, June 25, 2022 - 10:34:45 AM
Long-term archiving on: : Wednesday, August 6, 2014 - 1:25:24 PM


  • HAL Id : tel-00987686, version 1



Hervé Hocquard. Colorations de graphes sous contraintes. Mathématique discrète [cs.DM]. Université Sciences et Technologies - Bordeaux I, 2011. Français. ⟨NNT : ⟩. ⟨tel-00987686⟩



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