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Article Dans Une Revue Graphs and Combinatorics Année : 2014

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

Résumé

Let 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.
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Dates et versions

hal-01285320 , version 1 (09-03-2016)

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  • HAL Id : hal-01285320 , version 1

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Lyes Dekar, Brice Effantin, Hamamache Kheddouci. [r,s,t]-colorings of graph products. Graphs and Combinatorics, 2014, 30 (5), pp.1135-1147. ⟨hal-01285320⟩
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