A Self-Stabilizing (delta+1)- Edge-Coloring Algorithm of Arbitrary Graphs.

International audienceGiven a graph G = (V,E), an edge-coloring of G is a function from the set of edges E to colors {1, 2, · · ·, k} such that any two adjacent edges are assigned different colors. In this paper, we propose a self-stabilizing edge-coloring algorithm in a polynomial number of moves. The protocol assumes the unfair central dæmon and the coloring is a (delta + 1)-edge-coloring of G, where delta is the maximum degree in G. To our knowledge, we give the first self-stabilizing edge-coloring algorithm using (delta+ 1) colors of arbitrary graphs

[r,s,t]-colorings of graph products

International audienceLet G = (V,E) be a graph with vertex set V and edge set E. Given non negative integers r, s and t, an [r, s, t]-coloring of a graph G is a proper total coloring where the neighboring elements of G (vertices and edges) receive colors with a certain difference r between colors of adjacent vertices, a difference s between colors of adjacent edges and a difference t between colors of a vertex and an incident edge. Thus [r, s, t]-colorings generalize the classical colorings of graphs and can have applications in different fields like scheduling, channel assignment problem, etc. The [r, s, t]-chromatic number of G is the minimum k such that G admits an [r, s, t]-coloring. In our paper we propose several bounds for the [r, s, t]-chromatic number of the cartesian and direct products of some graphs

[r,s,t]-colorings of graph products

International audienceLet G = (V,E) be a graph with vertex set V and edge set E. Given non negative integers r, s and t, an [r, s, t]-coloring of a graph G is a proper total coloring where the neighboring elements of G (vertices and edges) receive colors with a certain difference r between colors of adjacent vertices, a difference s between colors of adjacent edges and a difference t between colors of a vertex and an incident edge. Thus [r, s, t]-colorings generalize the classical colorings of graphs and can have applications in different fields like scheduling, channel assignment problem, etc. The [r, s, t]-chromatic number of G is the minimum k such that G admits an [r, s, t]-coloring. In our paper we propose several bounds for the [r, s, t]-chromatic number of the cartesian and direct products of some graphs