On interval edge-colorings of outerplanar graphs

List Edge Colorings of Outerplanar Graphs

Graphs and colors : edge-colored graphs, edge-colorings and proper connections. (Graphes et couleurs : graphes arêtes-coloriés, coloration d'arêtes et connexité propre)

In this thesis, we study different problems in edge-colored graphs and edge-colored multigraphs, such as proper connection, strong edge colorings, and proper hamiltonian paths and cycles. Finally, we improve the known O(n) algorithm to decide the behavior of a graph under the biclique operator, by studying bicliques in graphs without false-twin vertices. In particular, • We first study the k-pr...

On the cost chromatic number of outerplanar, planar, and line graphs

We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost c...

On Group Choosability of Total Graphs

In this paper, we study the group and list group colorings of total graphs and present group coloring versions of the total and list total colorings conjectures.We establish the group coloring version of the total coloring conjecture for the following classes of graphs: graphs with small maximum degree, two-degenerate graphs, planner graphs with maximum degree at least 11, planner graphs withou...

Vertex-Coloring with Defects

Defective coloring is a variant of the traditional vertex-coloring in which adjacent vertices are allowed to have the same color, as long as the induced monochromatic components have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, diameter, and acyc...